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Book synopsis

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. TOC: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.

Book details

Book category Books in English Mathematics & science Mathematics Algebra

• Full title: Linear Algebraic Monoids
• Author: Lex E. Renner
• Language: English
• Binding: Hardback
• Number of pages: 246
• EAN: 9783540242413
• ISBN: 3540242414
• ID: 01560213
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 1200 g
• Dimensions: 235 × 155 × 22 mm
• Date of publishing: 11. March 2005

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