Modern Trends In Algebra And Representation Theory

Author : David Jordan,Nadia Mazza,Sibylle Schroll
Publisher : Cambridge University Press
Page : 407 pages
File Size : 51,8 Mb
Release : 2023-08-17
Category : Mathematics
ISBN : 9781009097352

Get Book

Modern Trends in Algebra and Representation Theory by David Jordan,Nadia Mazza,Sibylle Schroll Pdf

Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.

Author : HENNING KRAUSE; PETER LITTELMANN; GUNTER MALLE; KA.,Henning Krause
Publisher : Unknown
Page : 763 pages
File Size : 54,7 Mb
Release : 2017
Category : Categories (Mathematics)
ISBN : 3037196718

Get Book

Representation Theory by HENNING KRAUSE; PETER LITTELMANN; GUNTER MALLE; KA.,Henning Krause Pdf

From April 2009 until March 2016, the German Science Foundation supported generously the Priority Program SPP 1388 in Representation Theory. The core principles of the projects realized in the framework of the priority program have been categorification and geometrization, this is also reflected by the contributions to this volume. Apart from the articles by former postdocs supported by the priority program, the volume contains a number of invited research and survey articles, many of them are extended versions of talks given at the last joint meeting of the priority program in Bad Honnef in March 2015. This volume is covering current research topics from the representation theory of finite groups, of algebraic groups, of Lie superalgebras, of finite dimensional algebras and of infinite dimensional Lie groups. Graduate students and researchers in mathematics interested in representation theory will find this volume inspiring. It contains many stimulating contributions to the development of this broad and extremely diverse subject.

Author : Albert John Coleman,V. Futorny,Richard D. Pollack
Publisher : Kingston, Ont. : Queen's University
Page : 118 pages
File Size : 47,8 Mb
Release : 1994
Category : Mathematics
ISBN : OSU:32435050758267

Get Book

Modern Trends in Lie Algebra Representation Theory by Albert John Coleman,V. Futorny,Richard D. Pollack Pdf

Author : Anna Beliakova,Aaron D. Lauda
Publisher : American Mathematical Soc.
Page : 361 pages
File Size : 53,7 Mb
Release : 2017-02-21
Category : Algebra
ISBN : 9781470424602

Get Book

Categorification and Higher Representation Theory by Anna Beliakova,Aaron D. Lauda Pdf

The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory. This volume exhibits some of the current trends in higher representation theory and the diverse techniques that are being employed in this field with the aim of showcasing the many applications of higher representation theory. The companion volume (Contemporary Mathematics, Volume 684) is devoted to categorification in geometry, topology, and physics.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 53,5 Mb
Release : 1998
Category : Associative algebras
ISBN : 0821855654

Get Book

Trends in the Representation Theory of Finite Dimensional Algebras by Anonim Pdf

Author : Ibrahim Assem,Christof Geiß,Sonia Trepode
Publisher : American Mathematical Soc.
Page : 257 pages
File Size : 41,9 Mb
Release : 2021-01-06
Category : Education
ISBN : 9781470451592

Get Book

Advances in Representation Theory of Algebras by Ibrahim Assem,Christof Geiß,Sonia Trepode Pdf

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.

Author : Jan Šťovíček,Jan Trlifaj
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 45,6 Mb
Release : 2020-11-13
Category : Education
ISBN : 9781470451318

Get Book

Representation Theory and Beyond by Jan Šťovíček,Jan Trlifaj Pdf

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.

Author : Kiyoshi Igusa,Alex Martsinkovsky,Gordana Todorov
Publisher : American Mathematical Soc.
Page : 241 pages
File Size : 55,9 Mb
Release : 2021-05-17
Category : Education
ISBN : 9781470452308

Get Book

Representations of Algebras, Geometry and Physics by Kiyoshi Igusa,Alex Martsinkovsky,Gordana Todorov Pdf

This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25–30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Reflecting recent developments in modern representation theory of algebras, the selected topics include an introduction to a new class of quiver algebras on surfaces, called “geodesic ghor algebras”, a detailed presentation of Feynman categories from a representation-theoretic viewpoint, connections between representations of quivers and the structure theory of Coxeter groups, powerful new applications of approximable triangulated categories, new results on the heart of a t t-structure, and an introduction to methods of constructive category theory.

Author : Luchezar L. Avramov,Mark Green,Craig Huneke,Karen E. Smith,Bernd Sturmfels
Publisher : Cambridge University Press
Page : 266 pages
File Size : 47,9 Mb
Release : 2011-04-14
Category : Mathematics
ISBN : 0521168724

Get Book

Trends in Commutative Algebra by Luchezar L. Avramov,Mark Green,Craig Huneke,Karen E. Smith,Bernd Sturmfels Pdf

This book is based on lectures by six internationally known experts presented at the 2002 MSRI introductory workshop on commutative algebra. They focus on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics, with all necessary background provided. Short complementary papers describing work at the research frontier are also included. The unusual scope and format make the book invaluable reading for graduate students and researchers interested in commutative algebra and its various uses.

Author : D. Benson
Publisher : Springer
Page : 246 pages
File Size : 40,8 Mb
Release : 2008-07-22
Category : Mathematics
ISBN : 9783540389408

Get Book

Modular Representation Theory by D. Benson Pdf

This reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.

Author : Kenneth W. Johnson
Publisher : Springer Nature
Page : 384 pages
File Size : 54,6 Mb
Release : 2019-11-08
Category : Mathematics
ISBN : 9783030283001

Get Book

Group Matrices, Group Determinants and Representation Theory by Kenneth W. Johnson Pdf

This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science. The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.

Author : Vladimir Baranovsky,Nicolas Guay,Travis Schedler
Publisher : Springer Nature
Page : 458 pages
File Size : 52,7 Mb
Release : 2022-06-15
Category : Mathematics
ISBN : 9783030820077

Get Book

Representation Theory and Algebraic Geometry by Vladimir Baranovsky,Nicolas Guay,Travis Schedler Pdf

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theory D-modules and perverse sheaves Analogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.

Author : Karl-Hermann Neeb,Arturo Pianzola
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 43,6 Mb
Release : 2010-10-17
Category : Mathematics
ISBN : 9780817647414

Get Book

Developments and Trends in Infinite-Dimensional Lie Theory by Karl-Hermann Neeb,Arturo Pianzola Pdf

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.

Author : Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 51,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511

Get Book

Introduction to Representation Theory by Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina Pdf

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Author : Vyjayanthi Chari,Jacob Greenstein,Kailash C. Misra,K. N. Raghavan,Sankaran Viswanath
Publisher : American Mathematical Soc.
Page : 222 pages
File Size : 54,6 Mb
Release : 2013-11-25
Category : Mathematics
ISBN : 9780821890370

Get Book

Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory by Vyjayanthi Chari,Jacob Greenstein,Kailash C. Misra,K. N. Raghavan,Sankaran Viswanath Pdf

This volume contains the proceedings of the International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, held August 12-16, 2010, at the National Institute of Advanced Studies, Bangalore, India, and the follow-up conference held May 18-20, 2012, at the University of California, USA. It contains original research and survey articles on various topics in the theory of representations of Lie algebras, quantum groups and algebraic groups, including crystal bases, categorification, toroidal algebras and their generalisations, vertex algebras, Hecke algebras, Kazhdan-Lusztig bases, $q$-Schur algebras, and Weyl algebras.