Series in Algebra - Vol. 6
SEMIGROUPS OF MATRICES
by Jan Okninski (Warsaw University)
This book is concerned with the structure of linear semigroups, that is, subsemigroups of the multiplicative semigroup Mn(K) of n ´ n matrices over a field K (or, more generally, skew linear semigroups — if K is allowed to be a division ring) and its applications to certain problems on associative algebras, semigroups and linear representations. It is motivated by several recent developments in the area of linear semigroups and their applications. It summarizes the state of knowledge in this area, presenting the results for the first time in a unified form. The book's point of departure is a structure theorem, which allows the use of powerful techniques of linear groups. Certain aspects of a combinatorial nature, connections with the theory of linear representations and applications to various problems on associative algebras are also discussed.
Contents:
- General Techniques
- Full Linear Monoid
- Structure of Linear
Semigroups
- Irreducible Semigroups
- Identities
- Generalised Tits Alternative
- Growth
- Monoids of Lie Type
- Applications
Readership: Pure mathematicians and computer scientists.
"The book presents the current state of knowledge in the area, collects in a convenient form many interesting recent results scattered in the literature, and provides new insights in various technical methods. Thus it is a most valuable text for researchers actively using matrices in their work."
| 328pp |
Pub. date: Aug 1998 |
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