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Linear Algebraic Monoids: (134 Encyclopaedia of Mathematical Sciences)

Linear Algebraic Monoids: (134 Encyclopaedia of Mathematical Sciences)


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About the Book

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.

Table 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.

Review :
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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Product Details
  • ISBN-13: 9783540242413
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 246
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 3540242414
  • Publisher Date: 11 Mar 2005
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: 134 Encyclopaedia of Mathematical Sciences


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Linear Algebraic Monoids: (134 Encyclopaedia of Mathematical Sciences)
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Linear Algebraic Monoids: (134 Encyclopaedia of Mathematical Sciences)
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