⁎-Superalgebras and exponential growth
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- 作者：Rafael Bezerra dos Santos1 ; rafaelsantos23@ufmg.br
- 关键词：primary ; 16R50 ; secondary ; 16R10 ; 16P90 ; 16W10
- 刊名：Journal of Algebra
- 出版年：2017
- 出版时间：1 March 2017
- 年：2017
- 卷：473
- 期：Complete
- 页码：283-306
- 全文大小：414 K
- 卷排序：473
文摘
In this paper, we study the exponential growth of ⁎-graded identities of a finite dimensional ⁎-superalgebra A over a field F of characteristic zero. If a ⁎-superalgebra A satisfies a non-trivial identity, then the sequence {cngri(A)}n≥1 of ⁎-graded codimensions of A is exponentially bounded and so we study the ⁎-graded exponent expgri(A):=limn→∞cngri(A)n of A . We show that expgri(A)=dimF(A)expgri(A)=dimF(A) if and only if A is a simple ⁎-superalgebra and F is the symmetric even center of A . Also, we characterize the finite dimensional ⁎-superalgebras such that expgri(A)≤1expgri(A)≤1 by the exclusion of four ⁎-superalgebras from vargri(A)vargri(A) and construct eleven ⁎-superalgebras Ei,i=1,…,11Ei,i=1,…,11, with the following property: expgri(A)>2expgri(A)>2 if and only if Ei∈vargri(A)Ei∈vargri(A), for some i∈{1,…,11}i∈{1,…,11}. As a consequence, we characterize the finite dimensional ⁎-superalgebras A such that expgri(A)=2expgri(A)=2.