Z(q)-graded identities and central polynomials of the Grassmann algebra

Author(s)

Guimaraes, Alan ; Fidelis, Claudemir ; Dias, Laise

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 609, p. 25-pg., 2021-01-15.

Abstract

Let F be an infinite field of characteristic p different from 2 and let E be the Grassmann algebra generated by an infinite dimensional vector space L over F. In this paper we provide, for any odd prime q, a finite basis for the T-q-ideal of the Z(q) -graded polynomial identities for E and a basis for the T-q space of graded central polynomials for E, for any Z(q)-grading on E such that L is homogeneous in the grading. Moreover, we prove that the set of all graded central polynomials of E is not finitely generated as a T-q-space, if p > 2. In the nonhomogeneous case such bases are also described when at least one non-neutral component has infinite many homogeneous elements of the basis of L in the respective grading. (C) 2020 Elsevier Inc. All rights reserved. (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