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Volume 30 Number 2-3 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1738

Title: Involution Matrix Algebras – Identities and Growth
Authors: Rashkova, Tsetska
Keywords: Involution
Polynomial Identities
Symmetric Variables
Skew-Symmetric Variables
Bergman Type Polynomials
Characters
Hilbert Series
Growth
Codimensions
Issue Date: 2004
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 30, No 2-3, (2004), 239p-282p
Abstract: The paper is a survey on involutions (anti-automorphisms of order two) of different kinds. Starting with the first systematic investigations on involutions of central simple algebras due to Albert the author emphasizes on their basic properties, the conditions on their existence and their correspondence with structural characteristics of the algebras. Focusing on matrix algebras a complete description of involutions of the first kind on Mn(F) is given. The full correspondence between an involution of any kind for an arbitrary central simple algebra A over a field F of characteristic 0 and an involution on Mn(A) specially defined is studied. The research mainly in the last 40 years concerning the basic properties of involutions applied to identities for matrix algebras is reviewed starting with the works of Amitsur, Rowen and including the newest results on the topic. The cocharactes, codimensions and growth of algebras with involutions are considered as well.
Description: 2000 Mathematics Subject Classification: 16R50, 16R10.
URI: http://hdl.handle.net/10525/1738
ISSN: 1310-6600
Appears in Collections:Volume 30 Number 2-3

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