Computational Methods for Representations of Groups and Algebras

Dräxler, P.|Michler, G.|Ringel, C. M.

ISBN 10: 3764360631 / ISBN 13: 9783764360634

Published by Springer, Basel|Birkhäuser Basel, 2004

About this Item

This book presents material from 3 survey lectures and 14 additional invited lectures given at the Euroconference Computational Methods for Representations of Groups and Algebras held at Essen University in April 1997. The purpose of this meeting was to p. Seller Inventory # 872223020

Bibliographic Details

Title: Computational Methods for Representations of...

Publisher: Springer, Basel|Birkhäuser Basel

Publication Date: 2004

Binding: Hardcover

Condition: New

About this title

Synopsis:

This book presents material from 3 survey lectures and 14 additional invited lectures given at the Euroconference "Computational Methods for Representations of Groups and Algebras" held at Essen University in April 1997. The purpose of this meeting was to provide a survey of general theoretical and computational methods and recent advances in the representation theory of groups and algebras. The foundations of these research areas were laid in survey articles by P. Dräxler and R. Nörenberg on "Classification problems in the representation theory of finite-dimensional algebras", R. A. Wilson on "Construction of finite matrix groups" and E. Green on "Noncommutative Gröbner bases, and projective resolutions". Furthermore, new applications of the computational methods in linear algebra to the revision of the classification of finite simple sporadic groups are presented. Computational tools (including high-performance computations on supercomputers) have become increasingly important for classification problems. They are also inevitable for the construction of projective resolutions of finitely generated modules over finite-dimensional algebras and the study of group cohomology and rings of invariants. A major part of this book is devoted to a survey of algorithms for computing special examples in the study of Grothendieck groups, quadratic forms and derived categories of finite-dimensional algebras. Open questions on Lie algebras, Bruhat orders, Coxeter groups and Kazhdan Lusztig polynomials are investigated with the aid of computer programs. The contents of this book provide an overview on the present state of the art. Therefore it will be very useful for graduate students and researchers in mathematics, computer science and physics.