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Linear Algebraic Monoids

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This book provides an introduction to the field of linear algebraic monoids. This subject represents a synthesis of ideas from the theory of algebraic groups, algebraic geometry, matrix theory and abstract semigroup theory. Since every representation of an algebraic group gives rise to an algebraic monoid, the objects of study do indeed arise naturally.

Author(s): Mohan S. Putcha
Series: London Mathematical Society Lecture Note Series 133
Publisher: Cambridge University Press
Year: 1988

Language: English
Pages: 184

Cover......Page 1
Title......Page 4
Copyright......Page 5
CONTENTS......Page 6
Preface......Page 7
Notation......Page 9
1. Abstract Semigroups......Page 12
2. Algebraic Geometry......Page 23
3. Linear Algebraic Semigroups......Page 29
4. Linear Algebraic Groups......Page 38
5. Connected Algebraic Semigroups......Page 53
6. Connected Algebraic Monoids......Page 59
7. Reductive Groups and Regular Semigroups......Page 80
8. Diagonal Monoids......Page 91
9. Cross-section Lattices......Page 100
10. c'-Structure......Page 108
11. Renner's Decomposition and Related Finite Semigroups......Page 120
12. Biordered Sets......Page 132
13. Tits Building......Page 140
14. The System of Idempotents......Page 146
15. /-irreducible and /-co-reducible Monoids......Page 157
16. Renner's Extension Principle and Classification......Page 167
References......Page 174
Index......Page 181