Z-graded polynomial identities of the Grassmann algebra

Author(s)

Guimaraes, Alan de Araujo ^[1] ; Koshlukov, Plamen ^[2]

Affiliation

^[1] Univ Fed Rio Grande do Norte, Dept Math, BR-59078970 Natal, RN - Brazil

^[2] Univ Estadual Campinas, Dept Math, 651 Sergio Buarque de Holanda, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 617, p. 190-214, MAY 15 2021.
• Web of Science Citations: 0

Abstract

Let F be an infinite field of characteristic different from 2, and let E be the Grassmann algebra of an infinite dimensional F-vector space L. In this paper we study the Z-graded polynomial identities of E with respect to certain Z-grading such that the vector space L is homogeneous in the grading. More precisely, we construct three types of Z-gradings on E, denoted by E-infinity, E-k{*} and E-k, and we give the explicit form of the corresponding Z-graded polynomial identities. We show that the homogeneous superalgebras E-infinity, E-k{*} and Ek studied in {[}12] can be obtained from E-infinity, E-k{*} and E-k as quotient gradings. Moreover we exhibit several other types of homogeneous Z-gradings on E, and describe their graded identities. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants