| Full text | |
| Author(s): |
Fideles, Claudemir
;
Gomes, Ana Beatriz
;
Grishkov, Alexandre
;
Guimaraes, Alan
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Linear Algebra and its Applications; v. 680, p. 15-pg., 2023-10-16. |
| Abstract | |
Let F be any field of characteristic different from two and let E be the Grassmann algebra of an infinite dimensional F-vector space L. In this paper we will provide a condition for a Z2-grading on E to behave like the natural Z2-grading Ecan. More specifically, our aim is to prove the validity of a weak version of a conjecture presented in [10]. The conjecture poses that every Z2-grading on E has at least one non-zero homogeneous element of L. As a consequence, we obtain a characterization of Ecan by means of its Z2-graded polynomial identities. Furthermore we construct a Z2-grading on E that gives a negative answer to the conjecture.(c) 2023 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 23/04011-9 - Struture of graded and/or trace algebras, and Invariant theory |
| Grantee: | Claudemir Fideles Bezerra Júnior |
| Support Opportunities: | Regular Research Grants |