Almost polynomial growth: Classifying varieties of graded algebras

作者：La Mattina Daniela^*

来源：Israel Journal of Mathematics, 2015, 207(1): 53-75.

DOI：10.1007/s11856-015-1171-y

Let G be a finite group, V a variety of associative G-graded algebras and c (n) (G) (V), n = 1, 2, aEuro broken vertical bar, its sequence of graded codimensions. It was recently shown by Valenti that such a sequence is polynomially bounded if and only if V does not contain a finite list of G-graded algebras. The list consists of group algebras of groups of order a prime number, the infinite-dimensional Grassmann algebra and the algebra of 2 x 2 upper triangular matrices with suitable gradings. Such algebras generate the only varieties of G-graded algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the G-graded varieties of almost polynomial growth by giving a complete list of finite-dimensional G-graded algebras generating them.

• 出版日期2015-4