Group graded algebras and almost polynomial growth

JOURNAL OF ALGEBRA

卷:334

Article

Valenti, Angela

关键词: Graded algebra;    Polynomial identity;    Growth;    Codimensions;   

DOI  :  10.1016/j.jalgebra.2011.03.004

来源: Elsevier

【 摘 要 】

Let F be a field of characteristic 0, G a finite abelian group and A a G-graded algebra. We prove that A generates a variety of G-graded algebras of almost polynomial growth if and only if A has the same graded identities as one of the following algebras: (1) FC(p), the group algebra of a cyclic group of order p, where p is a prime number and p vertical bar vertical bar G vertical bar; (2) UT(F), the algebra of 2 x 2 upper triangular matrices over F endowed with an elementary G-grading: (3) E. the infinite dimensional Grassmann algebra with trivial G-grading: (4) in case 2 vertical bar vertical bar G vertical bar, E(Z2), the Grassmann algebra with canonical Z(2)-grading. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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