The GK dimension of relatively free algebras of PI-algebras

Autor(es)

Centrone, Lucio

• Tipo de documento: Artigo Científico
• Fonte: Journal of Pure and Applied Algebra; v. 223, n. 7, p. 2977-2996, JUL 2019.
• Citações Web of Science: 0

Resumo

We prove a strict relation between the Gelfand-Kirillov (GK) dimension of the relatively free (graded) algebra of a PI-algebra and its (graded) exponent. As a consequence we show a Bahturin-Zaicev type result relating the GK dimension of the relatively free algebra of a graded PI-algebra and the one of its neutral part. We also get that the growth of the relatively free graded algebra of a matrix algebra is maximal when the grading is fine. Finally we compute the graded GK dimension of the matrix algebra with any grading and the graded GK dimension of any verbally prime algebra endowed with an elementary grading. (C) 2018 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 15/08961-5 - Crescimento de álgebras com identidades polinomiais
• Beneficiário: Lucio Centrone
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 18/02108-7 - Identidades em álgebras (não) associativas e temas afins.
• Beneficiário: Lucio Centrone
• Modalidade de apoio: Auxílio à Pesquisa - Regular