Encyclopaedia of Mathematical Sciences

By: Lex Renner

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Hardcover | 11 March 2005

At a Glance

Hardcover
260 Pages

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24.13 x 16.51 x 1.91

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The theory of linear algebraic monoids culminates in a coherent blend of algebraic groups, convex geometry, and semigroup theory. The book discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. An explicit cell decomposition is constructed for the wonderful compactification, as is a universal deformation for any semisimple group. A final chapter summarizes important connections with other areas of algebra and geometry. The book will serve as a solid basis for further research. Open problems are discussed as they arise and many useful exercises are included.

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"This account of algebraic monoids ... starts by recalling the basics of algebraic geometry, algebraic groups and semigroups ... . The main question, how a monoid is composed of units and idempotents, is discussed at length ... . A most useful account, giving current developments of the subject." (Mathematika, Vol. 52, 2005)

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You Can Find This Book In

Non-Fiction Mathematics Algebra Geometry Combinatorics & Graph Theory Discrete Mathematics

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Published: 12th February 2010

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Introduction
Background
Algebraic Monoids
Regularity Conditions
Classification of Reductive Monoids
Universal Constructions
Orbit Structure of Reductive Monoids
The Monoid Analogue of the Bruhat Decomposition
Representations and Blocks of Algebraic Monoids
Monoids of Lie Type
Cell Decomposition of Algebraic Monoids
Conjugacy Classes
The Centralizer of a Semisimple Element
Combinatorics Related to Algebraic Monoids
Related Developments
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Encyclopaedia of Mathematical Sciences

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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