Surveys In Representation Theory Of Algebras

Author : Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 49,6 Mb
Release : 2018-09-12
Category : Representations of algebras
ISBN : 9781470436797

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Surveys in Representation Theory of Algebras by Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov Pdf

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.

Author : Johan G. F. Belinfante,Bernard Kolman
Publisher : SIAM
Page : 175 pages
File Size : 48,8 Mb
Release : 1989-01-01
Category : Mathematics
ISBN : 1611971330

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A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods by Johan G. F. Belinfante,Bernard Kolman Pdf

Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.

Author : David J. Benson
Publisher : European Mathematical Society
Page : 1 pages
File Size : 55,8 Mb
Release : 2013
Category : Mathematics
ISBN : 9783037191255

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Advances in Representation Theory of Algebras by David J. Benson Pdf

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.

Author : R.L. Lipsman
Publisher : Springer
Page : 176 pages
File Size : 54,7 Mb
Release : 2006-08-01
Category : Mathematics
ISBN : 9783540384021

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Group Representations by R.L. Lipsman Pdf

Author : Andrzej Skowroński
Publisher : European Mathematical Society
Page : 732 pages
File Size : 52,9 Mb
Release : 2008
Category : Representations of algebras
ISBN : 3037190620

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Trends in Representation Theory of Algebras and Related Topics by Andrzej Skowroński Pdf

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.

Author : 3Island Press
Publisher : Unknown
Page : 536 pages
File Size : 55,7 Mb
Release : 1991-04-01
Category : Electronic
ISBN : 3034886594

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Representation Theory of Finite Groups and Finite-Dimensional Algebras by 3Island Press Pdf

Author : David J. Benson,Henning Krause,Andrzej Skowroński
Publisher : Unknown
Page : 367 pages
File Size : 47,9 Mb
Release : 2014
Category : MATHEMATICS
ISBN : 3037196254

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Advances in Representation Theory of Algebras by David J. Benson,Henning Krause,Andrzej Skowroński Pdf

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.

Author : Andrzej Skowroński,Kunio Yamagata
Publisher : European Mathematical Society
Page : 744 pages
File Size : 47,8 Mb
Release : 2011
Category : Algebra
ISBN : 3037191015

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Representations of Algebras and Related Topics by Andrzej Skowroński,Kunio Yamagata Pdf

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.

Author : Ragnar-Olaf Buchweitz,Helmut Lenzing
Publisher : American Mathematical Soc.
Page : 420 pages
File Size : 52,8 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821885928

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Representations of Algebras and Related Topics by Ragnar-Olaf Buchweitz,Helmut Lenzing Pdf

This proceedings volume resulted from the Tenth International Conference on Representations of Algebras and Related Topics held at The Fields Institute (Toronto, ON, Canada). The collection of research and survey articles, honoring Vlastimil Dlab's seventieth birthday, reflects state-of-the-art research on the topic. Leading experts contributed papers, demonstrating the interaction between representation theory of finite dimensional algebras and neighboring subjects. A wide range of topics are covered, including quantum groups, the theory of Lie algebras, the geometry and combinatorics of tilting theory, commutative algebra, algebraic geometry, homology theories, and derived and triangulated categories. The book is suitable for graduate students and researchers interested in the theory of algebras.

Author : Aslak Bakke Buan,Idun Reiten,Øyvind Solberg
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 49,8 Mb
Release : 2013-08-24
Category : Mathematics
ISBN : 9783642394850

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Algebras, Quivers and Representations by Aslak Bakke Buan,Idun Reiten,Øyvind Solberg Pdf

This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like, commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulate categories. ​

Author : Steven H. Weintraub
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 53,8 Mb
Release : 2003
Category : Finite groups
ISBN : 9780821832226

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Representation Theory of Finite Groups: Algebra and Arithmetic by Steven H. Weintraub Pdf

``We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his/her own.'' --from the Preface Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, representation theory has been one of the great tools in the study and classification of finite groups. There are some beautiful results that come from representation theory: Frobenius's Theorem, Burnside's Theorem, Artin's Theorem, Brauer's Theorem--all of which are covered in this textbook. Some seem uninspiring at first, but prove to be quite useful. Others are clearly deep from the outset. And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers. The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.

Author : Raymond C. Fabec
Publisher : CRC Press
Page : 448 pages
File Size : 46,6 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781482285772

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Fundamentals of Infinite Dimensional Representation Theory by Raymond C. Fabec Pdf

Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.

Author : Simon Gindikin,Semen Grigorʹevich Gindikin,Roe Goodman,Frederick P. Greenleaf,Paul J. Sally
Publisher : American Mathematical Soc.
Page : 256 pages
File Size : 53,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821803004

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Representation Theory and Analysis on Homogeneous Spaces by Simon Gindikin,Semen Grigorʹevich Gindikin,Roe Goodman,Frederick P. Greenleaf,Paul J. Sally Pdf

Combining presentation of new results with in-depth surveys of recent work, this book focuses on representation theory and harmonic analysis on real and $p$-adic groups. The papers are based on lectures presented at a conference dedicated to the memory of Larry Corwin and held at Rutgers University in February 1993. The book presents a survey of harmonic analysis on nilpotent homogeneous spaces, results on multiplicity formulas for induced representations, new methods for constructing unitary representations of real reductive groups, and a unified treatment of trace Paley-Wiener theorems for real and $p$-adic reductive groups.In the representation theory of the general linear group over $p$-adic fields, the book provides a description of Corwin's contributions, a survey of the role of Hecke algebras, and a presentation of the theory of simple types. Other types of reductive $p$-adic groups are also discussed. Among the other topics included are the representation theory of discrete rational nilpotent groups, skew-fields associated to quadratic algebras, and finite models for percolation. A timely publication featuring contributions by some of the top researchers in the field, this book offers a perspective not often found in conference proceedings.

Author : Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 48,5 Mb
Release : 1998
Category : Mathematics
ISBN : 0821808508

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Algebras and Modules I by Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society Pdf

Surveys developments in the representation theory of finite dimensional algebras and related topics in seven papers illustrating different techniques developed over the recent years. For graduate students and researchers with a background in commutative algebra, including rings, modules, and homological algebra. Suitable as a text for an advanced graduate course. No index. Member prices are $31 for institutions and $23 for individuals, and are available to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Giovanni Falcone
Publisher : Springer
Page : 361 pages
File Size : 42,8 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9783319621814

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Lie Groups, Differential Equations, and Geometry by Giovanni Falcone Pdf

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.