# Trends In Representation Theory Of Algebras And Related Topics

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## Trends in Representation Theory of Algebras and Related Topics

Author | : Andrzej Skowroński |

Publsiher | : European Mathematical Society |

Total Pages | : 710 |

Release | : 2008 |

ISBN | : 9783037190623 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Trends in Representation Theory of Algebras and Related Topics Book Excerpt:**

This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.

## Trends in Representation Theory of Algebras and Related Topics

Author | : José Antonio de la Peña,Raymundo Bautista |

Publsiher | : American Mathematical Soc. |

Total Pages | : 270 |

Release | : 2006 |

ISBN | : 0821838180 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Trends in Representation Theory of Algebras and Related Topics Book Excerpt:**

This book is based on lectures given during a Workshop on Representations of Algebras and Related Topics. Some additional articles are included in order to complete a panoramic view of the main trends of the subject. The volume contains original presentations by leading algebraists addressed to specialists as well as to a broader mathematical audience. The articles include new proofs, examples, and detailed arguments. Topics under discussion include moduli spaces associated to quivers, canonical basis of quantum algebras, categorifications and derived categories, $A$-infinity algebras and functor categories, cluster algebras, support varieties for modules and complexes, the Gabriel-Roiter measure for modules, and selfinjective algebras.

## Advances in Representation Theory of Algebras

Author | : Ibrahim Assem,Christof Geiß,Sonia Trepode |

Publsiher | : American Mathematical Soc. |

Total Pages | : 257 |

Release | : 2021-01-06 |

ISBN | : 147045159X |

Category | : Education |

Language | : EN, FR, DE, ES & NL |

**Advances in Representation Theory of Algebras Book Excerpt:**

The Seventh ARTA (“Advances in Representation Theory of Algebras VII”) conference took place at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México, in Mexico City, from September 24–28, 2018, in honor of José Antonio de la Peña's 60th birthday. Papers in this volume cover topics Professor de la Peña worked on, such as covering theory, tame algebras, and the use of quadratic forms in representation theory. Also included are papers on the categorical approach to representations of algebras and relations to Lie theory, Cohen–Macaulay modules, quantum groups and other algebraic structures.

## Introduction to the Representation Theory of Algebras

Author | : Michael Barot |

Publsiher | : Springer |

Total Pages | : 179 |

Release | : 2014-12-29 |

ISBN | : 3319114751 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Introduction to the Representation Theory of Algebras Book Excerpt:**

This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations, explaining the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander–Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel‘s Theorem, the trichotomy and the Theorem of Kac – all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.

## Lie Algebras Vertex Operator Algebras and Related Topics

Author | : Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr |

Publsiher | : American Mathematical Soc. |

Total Pages | : 274 |

Release | : 2017-08-15 |

ISBN | : 1470426668 |

Category | : Lie algebras |

Language | : EN, FR, DE, ES & NL |

**Lie Algebras Vertex Operator Algebras and Related Topics Book Excerpt:**

This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.

## TRENDS IN REPRESENTATION THEORY OF ALGEBRAS AND RELATED TOPICS

Author | : ANDRZEJ SKOWROSKI. |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 2022 |

ISBN | : 9783037195628 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**TRENDS IN REPRESENTATION THEORY OF ALGEBRAS AND RELATED TOPICS Book Excerpt:**

## Homological Methods Representation Theory and Cluster Algebras

Author | : Ibrahim Assem,Sonia Trepode |

Publsiher | : Springer |

Total Pages | : 223 |

Release | : 2018-04-18 |

ISBN | : 3319745859 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Homological Methods Representation Theory and Cluster Algebras Book Excerpt:**

This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study. The six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck. The courses held were: Advanced homological algebra Introduction to the representation theory of algebras Auslander-Reiten theory for algebras of infinite representation type Cluster algebras arising from surfaces Cluster tilted algebras Cluster characters Introduction to K-theory Brauer graph algebras and applications to cluster algebras

## Surveys in Representation Theory of Algebras

Author | : Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov |

Publsiher | : American Mathematical Soc. |

Total Pages | : 203 |

Release | : 2018-09-12 |

ISBN | : 1470436795 |

Category | : Representations of algebras |

Language | : EN, FR, DE, ES & NL |

**Surveys in Representation Theory of Algebras Book Excerpt:**

This volume contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years. Reflecting the diverse landscape of modern representation theory of algebras, the selected articles include: a quick introduction to silting modules; a survey on the first decade of co-t-structures in triangulated categories; a functorial approach to the notion of module; a representation-theoretic approach to recollements in abelian categories; new examples of applications of relative homological algebra; connections between Coxeter groups and quiver representations; and recent progress on limits of approximation theory.

## Interactions Between Homotopy Theory and Algebra

Author | : Luchezar L. Avramov |

Publsiher | : American Mathematical Soc. |

Total Pages | : 334 |

Release | : 2007 |

ISBN | : 0821838148 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Interactions Between Homotopy Theory and Algebra Book Excerpt:**

This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.

## Representations of Algebras and Related Topics

Author | : Andrzej Skowroński,Kunio Yamagata |

Publsiher | : European Mathematical Society |

Total Pages | : 728 |

Release | : 2011 |

ISBN | : 9783037191019 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Representations of Algebras and Related Topics Book Excerpt:**

This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.

## Geometric and Topological Aspects of the Representation Theory of Finite Groups

Author | : Jon F. Carlson,Srikanth B. Iyengar,Julia Pevtsova |

Publsiher | : Springer |

Total Pages | : 495 |

Release | : 2018-10-04 |

ISBN | : 3319940333 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Geometric and Topological Aspects of the Representation Theory of Finite Groups Book Excerpt:**

These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.

## Representation Theory of Algebras and Related Topics

Author | : Raymundo Bautista,Roberto Martínez-Villa,José Antonio de la Peña,Workshop on Representation Theory of Algebras and Related Topics (1994 : Mexico City, Mexico) |

Publsiher | : American Mathematical Soc. |

Total Pages | : 406 |

Release | : 1996 |

ISBN | : 9780821803967 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Representation Theory of Algebras and Related Topics Book Excerpt:**

These proceedings report a number of lecture series delivered during the Workshop on Representation Theory of Algebras and Related Topics held at Universidad Nacional Autonoma de Mexico (UNAM) in August 1994. The workshop was dedicated to recent advances in the field and its interaction with other areas of mathematics, such as algebraic geometry, ring theory, and representation of groups. The program of the Workshop consisted of 9 lecture series. In addition there was a Tame Day consisting of 6 lectures reporting on the recent advances in the study of tame algebras and their module categories. During the Workshop there was a session devoted to the exhibition of computer programs developed by participants. These programs are implementations of algorithms related to the calculation of important aspects of algebras and their module categories.

## Expository Lectures on Representation Theory

Author | : Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov |

Publsiher | : American Mathematical Soc. |

Total Pages | : 224 |

Release | : 2014-01-16 |

ISBN | : 0821891405 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Expository Lectures on Representation Theory Book Excerpt:**

This volume contains the proceedings of the Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2012, in Falmouth, MA. The representation theory of finite dimensional algebras and related topics, especially cluster combinatorics, is a very active topic of research. This volume contains papers covering both the history and the latest developments in this topic. In particular, Otto Kerner gives a review of basic theorems and latest results about wild hereditary algebras, Yuri Berest develops the theory of derived representation schemes, and Markus Schmidmeier presents new applications of arc diagrams.

## Representations of Algebraic Groups Quantum Groups and Lie Algebras

Author | : Georgia Benkart |

Publsiher | : American Mathematical Soc. |

Total Pages | : 254 |

Release | : 2006 |

ISBN | : 0821839241 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Representations of Algebraic Groups Quantum Groups and Lie Algebras Book Excerpt:**

The book contains several well-written, accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. Geometric methods have been instrumental in representation theory, and these proceedings include surveys on geometric as well as combinatorial constructions of the crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic, left cells in two sided cells of affine Weyl groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the interaction of many different research areas and should be helpful to those who want to have a glimpse of current research involving representation theory.

## Representation Theory and Beyond

Author | : Jan Šťovíček,Jan Trlifaj |

Publsiher | : American Mathematical Soc. |

Total Pages | : 298 |

Release | : 2020-11-13 |

ISBN | : 147045131X |

Category | : Education |

Language | : EN, FR, DE, ES & NL |

**Representation Theory and Beyond Book Excerpt:**

This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.

## Large Deviations for Additive Functionals of Markov Chains

Author | : Palle E. T. Jørgensen |

Publsiher | : American Mathematical Soc. |

Total Pages | : 417 |

Release | : 2006 |

ISBN | : 0821839233 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Large Deviations for Additive Functionals of Markov Chains Book Excerpt:**

This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C^*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.

## Recent Trends in Partial Differential Equations

Author | : Xavier Cabré,José Antonio Carrillo |

Publsiher | : American Mathematical Soc. |

Total Pages | : 123 |

Release | : 2006 |

ISBN | : 0821838911 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Recent Trends in Partial Differential Equations Book Excerpt:**

"The research and expository articles for courses and talks given at the 'UIMP-RSME Lluis A. Santaló Summer School' with title 'Recent Trends in Partial Differential Equations'."--Pref.

## Recent Developments in Quantum Affine Algebras and Related Topics

Author | : Naihuan Jing,Kailash C. Misra |

Publsiher | : American Mathematical Soc. |

Total Pages | : 469 |

Release | : 1999 |

ISBN | : 0821811991 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Recent Developments in Quantum Affine Algebras and Related Topics Book Excerpt:**

This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying 'center stage' in the theory of infinite dimensional Lie theory.

## Maximal Cohen Macaulay Modules Over Non Isolated Surface Singularities and Matrix Problems

Author | : Igor Burban,Yuriy Drozd |

Publsiher | : American Mathematical Soc. |

Total Pages | : 114 |

Release | : 2017-07-13 |

ISBN | : 1470425378 |

Category | : Cohen-Macaulay modules |

Language | : EN, FR, DE, ES & NL |

**Maximal Cohen Macaulay Modules Over Non Isolated Surface Singularities and Matrix Problems Book Excerpt:**

In this article the authors develop a new method to deal with maximal Cohen–Macaulay modules over non–isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen–Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen–Macaulay representation type. The authors' approach is illustrated on the case of k as well as several other rings. This study of maximal Cohen–Macaulay modules over non–isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.

## Inverse Problems Multi scale Analysis and Effective Medium Theory

Author | : Habib Ammari,Hyeonbae Kang |

Publsiher | : American Mathematical Soc. |

Total Pages | : 265 |

Release | : 2006 |

ISBN | : 0821839683 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Inverse Problems Multi scale Analysis and Effective Medium Theory Book Excerpt:**

Recent developments in inverse problems, multi-scale analysis and effective medium theory reveal that these fields share several fundamental concepts. This book is the proceedings of the research conference, ``Workshop in Seoul: Inverse Problems, Multi-Scale Analysis and Homogenization,'' held at Seoul National University, June 22-24, 2005. It highlights the benefits of sharing ideas among these areas, of merging the expertise of scientists working there, and of directing interest towards challenging issues such as imaging nanoscience and biological imaging. Contributions are written by prominent experts and are of interest to researchers and graduate students interested in partial differential equations and applications.