Involution Matrix Algebras – Identities and Growth

Rashkova, Tsetska. "Involution Matrix Algebras – Identities and Growth." Serdica Mathematical Journal 30.2-3 (2004): 239-282. <http://eudml.org/doc/219580>.

@article{Rashkova2004,
abstract = {2000 Mathematics Subject Classification: 16R50, 16R10.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.Partially supported by Grant MM1106/2001 of the Bulgarian Foundation for Scientific Research.},
author = {Rashkova, Tsetska},
journal = {Serdica Mathematical Journal},
keywords = {Involution; Polynomial Identities; Symmetric Variables; Skew-Symmetric Variables; Bergman Type Polynomials; Characters; Hilbert Series; Growth; Codimensions; algebras with involution; *-polynomial identities; Bergman type polynomial identities; cocharacters; growth of codimensions; central simple algebras; matrix algebras},
language = {eng},
number = {2-3},
pages = {239-282},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Involution Matrix Algebras – Identities and Growth},
url = {http://eudml.org/doc/219580},
volume = {30},
year = {2004},
}

TY - JOUR
AU - Rashkova, Tsetska
TI - Involution Matrix Algebras – Identities and Growth
JO - Serdica Mathematical Journal
PY - 2004
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 30
IS - 2-3
SP - 239
EP - 282
AB - 2000 Mathematics Subject Classification: 16R50, 16R10.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.Partially supported by Grant MM1106/2001 of the Bulgarian Foundation for Scientific Research.
LA - eng
KW - Involution; Polynomial Identities; Symmetric Variables; Skew-Symmetric Variables; Bergman Type Polynomials; Characters; Hilbert Series; Growth; Codimensions; algebras with involution; *-polynomial identities; Bergman type polynomial identities; cocharacters; growth of codimensions; central simple algebras; matrix algebras
UR - http://eudml.org/doc/219580
ER -