Identities and central polynomials with involution for the Grassmann algebra

Author(s)

Centrone, Lucio ^{[1, 2]} ; Goncalves, Dimas Jose ^[3] ; Silva, Dalton Couto ^[4]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Univ Bari Aldo Moro, Campus Univ Ernesto Quagliarello, Via E Orabona 4, I-70125 Bari - Italy

^[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

^[4] Inst Fed Educ Ciencia & Tecnol Sao Paulo, BR-11665071 Caraguatatuba, SP - Brazil

• Document type: Journal article
• Source: Journal of Algebra; v. 560, p. 219-240, OCT 15 2020.
• Web of Science Citations: 0

Abstract

Let E be the infinite dimensional Grassmann algebra over an infinite field of characteristic p different from 2. Given an involution phi on E, denote by Id(E,phi) and C(E,phi) the set of all {*}-polynomial identities and {*}-central polynomials of (E,phi) respectively. In this paper we describe Id(E,phi) and C(E,phi). Moreover, we prove that C(E,phi) is not finitely generated as a T({*})-space if p > 2. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 18/02108-7 - Identities in (non) associative algebras and related themes.
• Grantee: Lucio Centrone
• Support Opportunities: Regular Research Grants
• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants