A characterization of the natural grading of the Grassmann algebra and its non-homogeneous Z2-gradings

Autor(es)

Fideles, Claudemir ; Gomes, Ana Beatriz ; Grishkov, Alexandre ; Guimaraes, Alan

• Tipo de documento: Artigo Científico
• Fonte: Linear Algebra and its Applications; v. 680, p. 15-pg., 2023-10-16.

Resumo

Let F be any field of characteristic different from two and let E be the Grassmann algebra of an infinite dimensional F-vector space L. In this paper we will provide a condition for a Z2-grading on E to behave like the natural Z2-grading Ecan. More specifically, our aim is to prove the validity of a weak version of a conjecture presented in [10]. The conjecture poses that every Z2-grading on E has at least one non-zero homogeneous element of L. As a consequence, we obtain a characterization of Ecan by means of its Z2-graded polynomial identities. Furthermore we construct a Z2-grading on E that gives a negative answer to the conjecture.(c) 2023 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 23/04011-9 - Estrutura de álgebra graduadas e/ou com traço, e teoria dos Invariantes
• Beneficiário: Claudemir Fideles Bezerra Júnior
• Modalidade de apoio: Auxílio à Pesquisa - Regular