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TitleDefining relations of the noncommutative trace algebra of two matrices
Author(s) Francesca Benanti, Vesselin Drensky
TypeArticle in Journal
AbstractThe noncommutative (or mixed) trace algebra T n d is generated by d generic n × n matrices and by the algebra C n d generated by all traces of products of generic matrices, n , d ⩾ 2 . It is known that over a field of characteristic 0 this algebra is a finitely generated free module over a polynomial subalgebra S of the center C n d . For n = 3 and d = 2 we have found explicitly such a subalgebra S and a set of free generators of the S-module T 32 . We give also a set of defining relations of T 32 as an algebra and a Gröbner basis of the corresponding ideal. The proofs are based on easy computer calculations with standard functions of Maple, the explicit presentation of C 32 in terms of generators and relations, and methods of representation theory of the general linear group.
KeywordsGeneric matrices, Matrix invariants and concomitants, Trace algebras, Defining relations, Gröbner basis
ISSN0196-8858
URL http://www.sciencedirect.com/science/article/pii/S0196885806000431
LanguageEnglish
JournalAdvances in Applied Mathematics
Volume37
Number2
Pages162 - 182
Year2006
NoteSpecial issue in honor of Amitai Regev on his 65th birthday
Edition0
Translation No
Refereed No
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