GRADED IDENTITIES FOR ALGEBRAS WITH ELEMENTARY GRADINGS OVER AN INFINITE FIELD

Author(s)

Diniz, Diogo ^[1] ; Fidelis, Claudemir ^{[2, 1]} ; Koshlukov, Plamen ^[3]

Affiliation

^[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429970 Campina Grande, Paraiba - Brazil

^[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; JAN 2022.
• Web of Science Citations: 0

Abstract

Let F be an infinite field of positive characteristic p > 2 and let G be a group. In this paper, we study the graded identities satisfied by an associative algebra equipped with an elementary G-grading. Let E be the infinite-dimensional Grassmann algebra. For every a, b is an element of N we provide a basis for the graded polynomial identities, up to graded monomial identities, for the verbally prime algebras M-a,M-b (E), as well as their tensor products, with their elementary gradings. Moreover, we give an alternative proof of the fact that the tensor product M-a,M-b (E) circle times M-r,M-s (E) and M-ar+bs,M-as+br (E) are F-algebras which are not. PI equivalent.. Actually, we prove that the T-G-ideal of the former algebra is contained in the T-G-ideal of the latter. Furthermore, the inclusion is proper. Recall that it is well known that these algebras satisfy the same multilinear identities and hence in characteristic 0 they are PI equivalent. (AU)

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