Trace identities and almost polynomial growth

Autor(es)

Ioppolo, Antonio ; Koshlukov, Plamen ; La Mattina, Daniela

• Tipo de documento: Artigo Científico
• Fonte: Journal of Pure and Applied Algebra; v. 225, n. 2, p. 20-pg., 2021-02-01.

Resumo

In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: D-2, the algebra of 2 x 2 diagonal matrices and C-2, the algebra of 2 x 2 matrices generated by e(11) + e(22) and e(12). We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 18/17464-3 - Identidades polinomiais e superinvoluções
• Beneficiário: Antonio Ioppolo
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático