Advances in Representation Theory of Algebras

Advances in Representation Theory of Algebras
Author: Ibrahim Assem
Publisher: American Mathematical Soc.
Total Pages: 257
Release: 2021-01-06
Genre: Education
ISBN: 147045159X

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.

Sheaves on Manifolds

Sheaves on Manifolds
Author: Masaki Kashiwara
Publisher: Springer Science & Business Media
Total Pages: 522
Release: 2013-03-14
Genre: Mathematics
ISBN: 3662026619

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.

Handbook of Tilting Theory

Handbook of Tilting Theory
Author: Lidia Angeleri Hügel
Publisher: Cambridge University Press
Total Pages: 482
Release: 2007-01-04
Genre: Mathematics
ISBN: 9780521680455

A handbook of key articles providing both an introduction and reference for newcomers and experts alike.

Elements of the Representation Theory of Associative Algebras: Volume 1

Elements of the Representation Theory of Associative Algebras: Volume 1
Author: Ibrahim Assem
Publisher: Cambridge University Press
Total Pages: 480
Release: 2006-02-13
Genre: Mathematics
ISBN: 9780521584234

This is the first of a two-volume set that provides a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers and homological algebra. The treatment is self-contained and provides an elementary and up-to-date introduction to the subject using quiver-theoretical techniques and the theory of almost split sequences as well as tilting theory and the use of integral quadratic forms. Much of this material has never appeared before in book form. The book is primarily addressed to graduate students starting research in the representation theory of algebras, but it will also be of interest to mathematicians in other fields. The text includes many illustrative examples and a large number of exercises at the end of each of the ten chapters. Proofs are presented in complete detail, making the book suitable for courses, seminars, and self-study. Book jacket.

Discrete Painlevé Equations

Discrete Painlevé Equations
Author: Nalini Joshi
Publisher: American Mathematical Soc.
Total Pages: 154
Release: 2019-05-30
Genre: Mathematics
ISBN: 1470450380

Discrete Painlevé equations are nonlinear difference equations, which arise from translations on crystallographic lattices. The deceptive simplicity of this statement hides immensely rich mathematical properties, connecting dynamical systems, algebraic geometry, Coxeter groups, topology, special functions theory, and mathematical physics. This book necessarily starts with introductory material to give the reader an accessible entry point to this vast subject matter. It is based on lectures that the author presented as principal lecturer at a Conference Board of Mathematical Sciences and National Science Foundation conference in Texas in 2016. Instead of technical theorems or complete proofs, the book relies on providing essential points of many arguments through explicit examples, with the hope that they will be useful for applied mathematicians and physicists.

Higher Segal Spaces

Higher Segal Spaces
Author: Tobias Dyckerhoff
Publisher: Springer Nature
Total Pages: 230
Release: 2019-10-17
Genre: Mathematics
ISBN: 3030271242

This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of d-dimensional cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen’s S-construction, Hecke-Waldhausen constructions, and configuration spaces of flags. The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed. Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with a basic background in homotopy theory. A chapter on Bousfield localizations provides a transition to the general theory, formulated in terms of combinatorial model categories, that features in the main part of the book. Numerous examples throughout assist readers entering this exciting field to move toward active research; established researchers in the area will appreciate this work as a reference.

Formal Power Series and Algebraic Combinatorics

Formal Power Series and Algebraic Combinatorics
Author: Daniel Krob
Publisher: Springer Science & Business Media
Total Pages: 844
Release: 2000-05-26
Genre: Computers
ISBN: 9783540672470

This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...