Linear Algebraic Monoids [Paperback]

This book provides an introduction to the field of linear algebraic monoids.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.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.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.1. Abstract Semigroups; 2. Algebraic Geometry ; 3. Linear Algebraic Semigroups; 4. Linear Algebraic Groups; 5. Connected Algebraic Semigroups; 6. Connected Algebraic Monoids; 7. Reductive Groups and Regular Semigroups; 8. Diagonal Monoids; 9. Cross-section Lattices; 10. ?-Structure; 11. Renner's Decomposition and Related Finite Semigroups; 12. Biordered Sets; 13. Tits Building; 14. The System of Idempotents; 15. J-irreducible and J co-reducible Monoids; 16. Renner's Extension Principle and Classification.