Z-gradings on the Grassmann algebra over infinite fields: Graded identities and central polynomials

Author(s)

Fideles, Claudemir ; Guimaraes, Alan

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 33, n. 08, p. 23-pg., 2023-11-09.

Abstract

Let E be the infinite-dimensional Grassmann algebra over an infinite field F of characteristic different from 2. The main purpose of this paper is to describe the T-Z-ideal of the graded polynomial identities and the T-Z-space of the central polynomials of E equipped with its 2 and 3-induced Z-gradings. Therefore, we generalize the results of [A. Brandao, C. Fidelis and A. Guimaraes, Z-gradings of full support on the Grassmann algebra, J. Algebra 601 (2022) 332-353; C. Fidelis, A. Guimaraes and P. Koshlukov, A note on Z-gradings on the Grassmann algebra and elementary number theory, Linear Multilinear Algebra 71(7) (2023) 1244-1264] in the PI theory context. (AU)

• FAPESP's process: 23/04011-9 - Struture of graded and/or trace algebras, and Invariant theory
• Grantee: Claudemir Fideles Bezerra Júnior
• Support Opportunities: Regular Research Grants
• 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