Z-graded identities on the infinite-dimensional Grassmann algebra and arithmetic tools: revisited

Author(s)

Fidelis, Claudemir

• Document type: Journal article
• Source: TURKISH JOURNAL OF MATHEMATICS; v. N/A, p. 14-pg., 2022-03-09.

Abstract

The main purpose of this paper is to provide a survey of results concerning the Z-gradings on the infinite-dimensional Grassmann algebra E over a field of characteristic zero. First, we provide graded identities and central polynomials for E equipped with fine gradings on E by the semigroup (Z*, x). We also describe briefly techniques in order to illustrate some important methods to exhibit graded identities and central polynomials of E for other abelian groups. In particular, over a field of characteristic zero, so-called 2-induced gradings of full support were considered. In order to obtain these descriptions, we strongly use elementary number theory as a tool, providing an interesting connection between this area and PI-Theory. (AU)

• FAPESP's process: 19/12498-0 - Graded polynomial identities and identity with trace, and invariant theory
• Grantee: Claudemir Fideles Bezerra Júnior
• Support Opportunities: Scholarships in Brazil - Post-Doctoral