| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 34, I-90123 Palermo - Italy
[2] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05315970 Sao Paulo - Brazil
[3] Univ Fed ABC, Av Estados 5001, Santo Andre, SP - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 373, n. 11, p. 7869-7899, NOV 2020. |
| Web of Science Citations: | 1 |
| Abstract | |
We introduce the notion of star-fundamental algebra over a field of characteristic zero. We prove that in the framework of the theory of polynomial identities, these algebras are the building blocks of a finite dimensional algebra with involution {*}. To any star-algebra A is attached a numerical sequence c(n){*}(A), n >= 1, called the sequence of {*}- codimensions of A. Its asymptotic is an invariant giving a measure of the {*}- polynomial identities satisfied by A. It is well known that for a PI-algebra such a sequence is exponentially bounded and exp{*}(A) = limn(n ->infinity) n root c(n){*}(A) can be explicitly computed. Here we prove that if A is a star-fundamental algebra, C(1)n(t) exp{*} (A)n <= c(n){*}(A) <= C(2)n(t) exp{*} (A)(n), where C-1 > 0, C-2, t are constants and t is explicitly computed as a linear function of the dimension of the skew semisimple part of A and the nilpotency index of the Jacobson radical of A. We also prove that any finite dimensional star-algebra has the same {*}- identities as a finite direct sum of star-fundamental algebras. As a consequence, by the main result in {[}J. Algebra 383 (2013), pp. 144-167] we get that if A is any finitely generated star-algebra satisfying a polynomial identity, then the above still holds and, so, lim(n ->infinity) log(n) c(n){*} (A)/exp{*}(A)(n) exists and is an integer or half an integer. (AU) | |
| FAPESP's process: | 15/09162-9 - Non commutative algebra and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |