Polynomial codimension growth of algebras with involutions and superinvolutions

JOURNAL OF ALGEBRA

卷:472

Article

Ioppolo, Antonio¹  La Mattina, Daniela¹ 

[1] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 34, I-90123 Palermo, Italy

关键词: Polynomial identity;    Graded involution;    Superinvolution;    Growth;   

DOI  :  10.1016/j.jalgebra.2016.10.007

来源: Elsevier

【 摘 要 】

Let A be an associative algebra over a field F of characteristic zero endowed with a graded involution or a superinvolution * and let c*(n),(A) be its sequence of *-codimension. In [4,12] it was proved that if A is finite dimensional such sequence is polynomially bounded if and only if A generates a variety not containing a finite number of *-algebras: the group algebra of Z(2) and a 4-dimensional subalgebra of the 4 x 4 upper triangular matrices with suitable graded involutions or superinvolutions. In this paper we focus our attention on such algebras since they are the only finite dimensional *-algebras, up to TI-equivalence, generating varieties of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety has polynomial growth. We classify the subvarieties of such varieties by giving a complete list of generating finite dimensional *-algebras. Along the way we classify all minimal varieties of polynomial growth and surprisingly we show that their number is finite for any given growth. Finally we describe the *-algebras whose *-codimension are bounded by a linear function. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free