| Texto completo | |
| Autor(es): |
Giambruno, A.
;
La Mattina, D.
;
Milies, C. Polcino
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Algebra; v. 686, p. 19-pg., 2025-09-03. |
| Resumo | |
Let A be an algebra with involution * over a field of characteristic zero. There are three numerical sequences attached to the *-polynomial identities Id & lowast;(A) satisfied by A: the sequence of codimensions c & lowast;n(A), the sequence of central codimensions c & lowast;.z n(A) and the sequence of proper central codimensions c & lowast;,delta n (A) n = 1, 2, .... They give a measure of the *-polynomial identities, the central *-polynomials and the proper central *-polynomials of the algebra A. It has been proved ([9], [18]) that when A satisfies a nontrivial identity, the three sequences either grow exponentially or are polynomially bounded. Now, an algebra A has almost polynomial growth of the codimensions if c & lowast;n(A) grows exponentially and for any algebra B such that Id & lowast;(B) & supne; Id & lowast;(A), c & lowast;n(B) is polynomially bounded. Similarly we have the definitions of almost polynomial growth of the central codimensions c & lowast;.z n(A) and of the proper central codimensions c & lowast;,delta n (A). We aim to classify, up to *-PI-equivalence, the algebras with almost polynomial growth of one of the above codimensions. This has already been done in [8] regarding the codimensions c & lowast; n(A). Here we classify, up to *-PI-equivalence, the algebras having almost polynomial growth of the central *-polynomials by exhibiting three subalgebras of upper triangular matrices. We also construct three more finite dimensional algebras giving the classification of almost polynomial growth of the proper central *-polynomials. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU) | |
| Processo FAPESP: | 20/16594-0 - Anéis não comutativos e aplicações |
| Beneficiário: | Francisco Cesar Polcino Milies |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |