Semigroups of matrices
1. General techniques. 1.1. Semigroups and their algebras. 1.2. Zariski topology and closed semigroups. 1.3. Exterior power. 1.4. Combinatorial techniques -- 2. Full linear monoid. 2.1. Structure. 2.2. Idempotents and nil semigroups. 2.3. Combinatorics on [symbol] . 2.4. Complete reducibility of [symbol] -- 3. Structure of linear semigroups. 3.1. Uniform semigroups and associated groups. 3.2. Structure theorem. 3.3. Closure. 3.4.-simple semigroups. 3.5. Some reduction techniques -- 4. Irreducib…
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- Full title :Semigroups of matrices / Jan Okniński
Summary
1. General techniques. 1.1. Semigroups and their algebras. 1.2. Zariski topology and closed semigroups. 1.3. Exterior power. 1.4. Combinatorial techniques -- 2. Full linear monoid. 2.1. Structure. 2.2. Idempotents and nil semigroups. 2.3. Combinatorics on [symbol] . 2.4. Complete reducibility of [symbol] -- 3. Structure of linear semigroups. 3.1. Uniform semigroups and associated groups. 3.2. Structure theorem. 3.3. Closure. 3.4.-simple semigroups. 3.5. Some reduction techniques -- 4. Irreducible semigroups. 4.1. Structure. 4.2. Munn algebras and representations. 4.3. Irreducible representations. 4.4. Triangularizable semigroups -- 5. Identities. 5.1. Semigroup identities. 5.2. Al.most unipotent semigroups. 5.3. Nilpotent semigroups. 5.4. PI algebras -- 6. Generalised tits alternative. 6.1. Auxiliary results. 6.2. Free subsemigroups. 7. Growth. 7.1. Burnside theorem and some examples. 7.2. Linear growth and repetitivity. 7.3. Almost semisimple semigroups. 8. Monoids of Lie type -- 8.1. Definition and examples. 8.2. Universal monoids of Lie type. 8.3. Connections with group representations -- 9. Applications. 9.1. Skew linear semigroups and division algebras. 9.2. Graded rings: motivation and technical results. 9.3. Applications to graded rings
This book is concerned with the structure of linear semigroups, that is, subsemigroups of the multiplicative semigroup Mn(K) of n x 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
Edition Statements
- Publication Date:©1998
Publication Statements
- Publisher(s):World Scientific Pub. Co
- Place of Publication:Singapore
- Language:eng
- Publication Date:©1998
The Physical Object
- Description:1 Online-Ressource (xiv, 311 Seiten) : Illustrationen
Edition Identifiers
- ISBN:9810234457, 9789810234454, 9789812816290, 9812816291
- oclc:on1005227375
- Dewey Decimal:512/.2
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