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| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil
[2] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429970 Campina Grande, PB - Brazil
[3] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | ALGEBRAS AND REPRESENTATION THEORY; JUL 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
Let F be a field of characteristic zero and let R be an algebra that admits a regular grading by an abelian group H. Moreover, we consider G a group and let A be an algebra with a grading by the group G x H, we define the R-hull of A as the G x H-graded algebra given by R(A) = circle plus((g,h)is an element of G) (x) (H)A((g,h)) circle times R-h. In this paper we provide a basis for the graded identities (resp. central polynomials) of the R-hull of A, assuming that a (suitable) basis for the graded identities (resp. central polynomials) of the G x H-graded algebra A is known. In particular, for any a, b is an element of N, we find a basis for the graded identities and the graded central polynomials for the algebra M-a,M-b(E), graded by the group G x Z(2). Here E is the Grassmann algebra of an infinite dimensional F-vector space, equipped with its natural Z(2)-grading and the matrix algebra Ma+b(F) is equipped with an elementary grading by the group G x Z(2), so that its neutral component coincides with the subspace of the diagonal matrices. We describe the isomorphism classes of gradings on M-a,M-b(E) that arise in this way and count the isomorphism classes of such 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) is PI-equivalent to M-ar+bs,M-as+br(E). Finally, when the grading group is Z(3) x Z(2) (resp. Z x Z(2)), we present a complete description of a basis for the graded central polynomials for the algebra M-2,M-1(E) (resp. M-a,M-b(E) in the case b = 1). (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 |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |