Z-gradings of full support on the Grassmann algebra

Autor(es)

Brandao, Antonio ; Fidelis, Claudemir ; Guimaraes, Alan

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 601, p. 22-pg., 2022-07-01.

Resumo

Let E be the infinite dimensional Grassmann algebra over a field F of characteristic zero. In this paper we investigate the structures of Z-gradings on E of full support. Using methods of elementary number theory, we describe the Z graded polynomial identities for the so-called 2-induced Z-gradings on E of full support. As a consequence of this fact we provide examples of Z-gradings on E which are PI-equivalent but not Z-isomorphic. This is the first example of graded algebras with infinite support that are PI-equivalent, but non isomorphic as graded algebras. We also present the notion of central Z-gradings on E and we show that their Z-graded polynomial identities are closely related to the Z2-graded polynomial identities of E. (C)& nbsp;2022 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 19/12498-0 - Identidades polinomiais graduadas e com traço, e teoria dos invariantes
• Beneficiário: Claudemir Fideles Bezerra Júnior
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado