Linear Algebraic Monoids - ISBN:0521358094

Linear Algebraic Monoids

Date: 22 April 2011, 08:20

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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.
CONTENTS
Preface
Notation
1. Abstract Semigroups 1
2. Algebraic Geometry 12
3. Linear Algebraic Semigroups 18
4. Linear Algebraic Groups 27
5. Connected Algebraic Semigroups 42
6. Connected Algebraic Monoids 48
7. Reductive Groups and Regular Semigroups 69
8. Diagonal Monoids 80
9. Cross-section Lattices 89
10. c'-Structure 97
11. Renner's Decomposition and Related Finite Semigroups 109
12. Biordered Sets 121
13. Tits Building 129
14. The System of Idempotents 135
15. /-irreducible and /-co-reducible Monoids 146
16. Renner's Extension Principle and Classification 156
References 163
Index 170

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