On PI-algebras with additional structures: Rationality of Hilbert series and Specht's problem

Autor(es)

Centrone, Lucio ^{[1, 2]} ; Estrada, Alejandro ^[1] ; Ioppolo, Antonio ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Univ Bari Aldo Moro, Dipartimento Matemat, Via Edoardo Orabona 4, I-70125 Bari - Italy

^[3] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via R Cozzi 55, I-20126 Milan - Italy

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 592, p. 300-356, FEB 15 2022.
• Citações Web of Science: 0

Resumo

One of the main problems in PI-theory is to prove the rationality of the Hilbert series of the relatively free algebra of a given PI-algebra. In this paper we consider a field F of characteristic 0 and we prove the rationality of the Hilbert series of the PI-algebra A over F both in the case A is a superalgebra with superinvolution and when a finite dimensional semisimple Hopf algebra acts on A. Along the way, we give a proof of the Specht's problem in case A is a superalgebra with superinvolution. (c) 2021 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 18/17464-3 - Identidades polinomiais e superinvoluções
• Beneficiário: Antonio Ioppolo
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado