Linear Algebraic Monoids

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.

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)