Linear Algebraic Monoids

This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.

List of contents

Background.- Algebraic Monoids.- Regularity Conditions.- Classification of Reductive Monoids.- Universal Constructions.- Orbit Structure of Reductive Monoids.- The Analogue of the Bruhat Decomposition.- Representations and Blocks of Algebraic Monoids.- Monoids of Lie Type.- Cellular Decomposition of Algebraic Monoids.- Conjugacy Classes.- The Centralizer of a Semisimple Element.- Combinatorics Related to Algebraic Monoids.- Survey of Related Developments.

Summary

This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.

Additional text

From the reviews:

"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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From the reviews:

"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)

Product details

• Authors: Lex Renner, Lex E Renner, Lex E. Renner
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 06.10.2010
• EAN: 9783642063497
• ISBN: 978-3-642-06349-7
• No. of pages: 246
• Dimensions: 156 mm x 13 mm x 234 mm
• Weight: 399 g
• Illustrations: XII, 246 p. 5 illus.
• Series: Encyclopaedia of Mathematical Sciences; Encyclopaedia of Mathematical Sciences
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, Geometrie, B, Diskrete Mathematik, geometry, Combinatorics, Mathematics and Statistics, Linear Algebra, Discrete Mathematics, Combinatorics & graph theory, type map, torus embedding, reductive monoid