Finitely generated algebras with involution and multiplicities bounded by a constant

JOURNAL OF ALGEBRA

卷:422

Article

Vieira, A. C.

关键词: Algebras with involution;    Cocharacters;    Multiplicities and colength;   

DOI  :  10.1016/j.jalgebra.2014.09.016

来源: Elsevier

【 摘 要 】

Let A be an algebra with involution * over a field F of characteristic zero, and let chi(n)*(A), n = 1,2, ... , be the sequence of *-cocharacters of A. For every n >= 1, let l(n)*(A) denote the nth *-colength of A which is the sum of the multiplicities in chi(n)*(A). In this article, we classify in two different ways the finitely generated *-algebras satisfying an ordinary polynomial identity whose multiplicities of the *-cocharacters chi(n)*(A) are bounded by a constant. As a consequence this also yields a characterization of the *-varieties whose *-colength l(n)*(A), n = 1,2, ... , is bounded by a constant. (C) 2014 Elsevier Inc. All rights reserved.

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