Surveys in Representation Theory of 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.

Trends in Representation Theory of Algebras and Related Topics

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.

Trends in Representation Theory of Algebras and Related Topics

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.

A Survey of Knot Theory

A Survey of Knot Theory
Author: Akio Kawauchi
Publsiher: Birkhäuser
Total Pages: 423
Release: 2012-12-06
ISBN: 3034892276
Category: Mathematics
Language: EN, FR, DE, ES & NL

A Survey of Knot Theory Book Excerpt:

Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.

Cell Complexes Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry

Cell Complexes  Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry
Author: Stuart Margolis,Franco Saliola,Benjamin Steinberg
Publsiher: American Mathematical Society
Total Pages: 135
Release: 2021-12-30
ISBN: 1470450429
Category: Mathematics
Language: EN, FR, DE, ES & NL

Cell Complexes Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry Book Excerpt:

View the abstract.

Infinite dimensional Aspects of Representation Theory and Applications

Infinite dimensional Aspects of Representation Theory and Applications
Author: Stephen Berman
Publsiher: American Mathematical Soc.
Total Pages: 154
Release: 2005
ISBN: 082183701X
Category: Mathematics
Language: EN, FR, DE, ES & NL

Infinite dimensional Aspects of Representation Theory and Applications Book Excerpt:

The University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory.

Surveys in Representation Theory of Algebras

Surveys in Representation Theory of Algebras
Author: Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov
Publsiher: Unknown
Total Pages: 216
Release: 2018
ISBN: 9781470449032
Category: MATHEMATICS
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 betwe.

Schur Algebras and Representation Theory

Schur Algebras and Representation Theory
Author: Stuart Martin,Martin Stuart
Publsiher: Cambridge University Press
Total Pages: 232
Release: 1993
ISBN: 0521415918
Category: Mathematics
Language: EN, FR, DE, ES & NL

Schur Algebras and Representation Theory Book Excerpt:

This is the first comprehensive text in this important and active area of research.

Representation Theory of Finite Groups and Finite Dimensional Algebras

Representation Theory of Finite Groups and Finite Dimensional Algebras
Author: Michler,Ringel
Publsiher: Birkhäuser
Total Pages: 522
Release: 2012-12-06
ISBN: 3034886586
Category: Mathematics
Language: EN, FR, DE, ES & NL

Representation Theory of Finite Groups and Finite Dimensional Algebras Book Excerpt:

From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.

Recent Developments in Representation Theory

Recent Developments in Representation Theory
Author: Alex Martsinkovsky,Gordana Todorov,Kiyoshi Igusa
Publsiher: American Mathematical Soc.
Total Pages: 249
Release: 2016-08-26
ISBN: 1470419556
Category: Associative rings
Language: EN, FR, DE, ES & NL

Recent Developments in Representation Theory Book Excerpt:

This volume contains selected expository lectures delivered at the Maurice Auslander Distinguished Lectures and International Conference, held May 1–6, 2014, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Several significant developments of the last decade in representation theory of finite-dimensional algebras are related to combinatorics. Three of the five lectures in this volume deal, respectively, with the Catalan combinatorics, the combinatorics of Gelfand-Zetlin polytopes, and the combinatorics of tilting modules. The remaining papers present history and recent advances in the study of left orders in left Artinian rings and a survey on invariant theory of Artin-Schelter regular algebras.

Basic Representation Theory of Algebras

Basic Representation Theory of Algebras
Author: Ibrahim Assem,Flávio U. Coelho
Publsiher: Springer Nature
Total Pages: 311
Release: 2020-04-03
ISBN: 3030351181
Category: Mathematics
Language: EN, FR, DE, ES & NL

Basic Representation Theory of Algebras Book Excerpt:

This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander–Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander–Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.

Iwahori Hecke Algebras and their Representation Theory

Iwahori Hecke Algebras and their Representation Theory
Author: Ivan Cherednik,Yavor Markov,Roger E. Howe,George Lusztig
Publsiher: Springer
Total Pages: 114
Release: 2003-07-03
ISBN: 3540362053
Category: Mathematics
Language: EN, FR, DE, ES & NL

Iwahori Hecke Algebras and their Representation Theory Book Excerpt:

Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy.

Advances in Representation Theory of Algebras

Advances in Representation Theory of Algebras
Author: David J. Benson
Publsiher: European Mathematical Society
Total Pages: 367
Release: 2013
ISBN: 3037191252
Category: Mathematics
Language: EN, FR, DE, ES & NL

Advances in Representation Theory of Algebras Book Excerpt:

This volume presents a collection of articles devoted to representations of algebras and related topics. Dististinguished experts in this field presented their work at the International Conference on Representations of Algebras, which took place in Bielefeld in 2012. Many of the expository surveys are included here. Researchers of representation theory will find in this volume interesting and stimulating contributions to the development of the subject.

Advances in Representation Theory of Algebras

Advances in Representation Theory of Algebras
Author: David J. Benson,Henning Krause,Andrzej Skowroński
Publsiher: Unknown
Total Pages: 367
Release: 2014
ISBN: 9783037196250
Category: MATHEMATICS
Language: EN, FR, DE, ES & NL

Advances in Representation Theory of Algebras Book Excerpt:

This volume presents a collection of articles devoted to representations of algebras and related topics. Dististinguished experts in this field presented their work at the International Conference on Representations of Algebras which took place 2012 in Bielefeld. Many of the expository surveys are included here. Researchers of representation theory will find in this volume interesting and stimulating contributions to the development of the subject.

Expository Lectures on Representation Theory

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.

Representation Theory

Representation Theory
Author: Izrailʹ Moiseevich Gelʹfand
Publsiher: Cambridge University Press
Total Pages: 272
Release: 1982-11-18
ISBN: 0521289815
Category: Mathematics
Language: EN, FR, DE, ES & NL

Representation Theory Book Excerpt:

The unifying theme of this collection of papers by the very creative Russian mathematician I. M. Gelfand and his co-workers is the representation theory of groups and lattices. Two of the papers were inspired by application to theoretical physics; the others are pure mathematics though all the papers will interest mathematicians at quite opposite ends of the subject. Dr. G. Segal and Professor C-M. Ringel have written introductions to the papers which explain the background, put them in perspective and make them accessible to those with no specialist knowledge in the area.

Representations of Quantum Algebras and Combinatorics of Young Tableaux

Representations of Quantum Algebras and Combinatorics of Young Tableaux
Author: Susumu Ariki
Publsiher: American Mathematical Soc.
Total Pages: 158
Release: 2002
ISBN: 0821832328
Category: Mathematics
Language: EN, FR, DE, ES & NL

Representations of Quantum Algebras and Combinatorics of Young Tableaux Book Excerpt:

Another new title in the popular ULECT series; affordably-priced, softcover, advanced-level topics; presents a great entry point into a rapidly-developing topic area; self-contained and suitable for use as an independent study text.

Algebras and Modules I

Algebras and Modules I
Author: Idun Reiten,Sverre O. Smalø,Workshop on Representations of Algebras and Related Topics,Øyvind Solberg,Canadian Mathematical Society
Publsiher: American Mathematical Soc.
Total Pages: 198
Release: 1998
ISBN: 9780821808504
Category: Mathematics
Language: EN, FR, DE, ES & NL

Algebras and Modules I Book Excerpt:

This volume contains recent results on geometric aspects of representations of algebras, a thorough treatment of the theory of quasitilted algebras, new developments on infinite dimensional representations of finite dimensional algebras, a bridge between representation of algebraic groups and representation theory of finite dimensional algebras, and recent discoveries on modular representation theory. In addition, the volume contains two papers devoted to some of Maurice Auslander's many contributions both in the representation theory of finite dimensional algebras and in commutative ring theory. The invited contributions to this volume are based on lectures given by leading researchers in the field at the Workshop on Representations of Algebras and Related Topics, Trondheim, Norway. Features: a unique collection of survey papers containing old and new developments in the representation theory of finite dimensional algebras and related topics an outstanding source for examples of different techniques developed in recent years in this area of research papers presented with emphasis on clarity and readability A general background in noncommutative algebra including rings, modules and homological algebra is required. Given that, parts of this volume would be suitable as a textbook for an advanced graduate course in algebra.

A Survey of Modern Algebra

A Survey of Modern Algebra
Author: Garrett Birkhoff,Saunders Mac Lane
Publsiher: CRC Press
Total Pages: 512
Release: 2017-12-19
ISBN: 1351991736
Category: Mathematics
Language: EN, FR, DE, ES & NL

A Survey of Modern Algebra Book Excerpt:

This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.

Quadratic Forms in the Representation Theory of Finite Dimensional Algebras

Quadratic Forms in the Representation Theory of Finite Dimensional Algebras
Author: C. M. Ringel,Workshop Representation Theory
Publsiher: Unknown
Total Pages: 170
Release: 1995
ISBN: 1928374650XXX
Category: Electronic Book
Language: EN, FR, DE, ES & NL

Quadratic Forms in the Representation Theory of Finite Dimensional Algebras Book Excerpt: