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| Full text | |
| Author(s): |
Brandao, Antonio
;
Fidelis, Claudemir
;
Guimaraes, Alan
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Algebra; v. 601, p. 22-pg., 2022-07-01. |
| Abstract | |
Let E be the infinite dimensional Grassmann algebra over a field F of characteristic zero. In this paper we investigate the structures of Z-gradings on E of full support. Using methods of elementary number theory, we describe the Z graded polynomial identities for the so-called 2-induced Z-gradings on E of full support. As a consequence of this fact we provide examples of Z-gradings on E which are PI-equivalent but not Z-isomorphic. This is the first example of graded algebras with infinite support that are PI-equivalent, but non isomorphic as graded algebras. We also present the notion of central Z-gradings on E and we show that their Z-graded polynomial identities are closely related to the Z2-graded polynomial identities of E. (C)& nbsp;2022 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 |