Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8966117 | Journal of Pure and Applied Algebra | 2019 | 14 Pages |
Abstract
In this paper we generalize the concepts of good and elementary gradings for an associative algebra A with a fixed multiplicative basis B. When the group G considered in the grading is abelian, we equip the set of good G-gradings of A with a structure of abelian group, which is denoted by G(B,G). Moreover, when A admits elementary G-gradings, we show the set E(B,G) of all elementary G-gradings of A is a subgroup of G(B,G). In this case, we introduce a cohomology for the pair (A,B) and we show that G(B,G)/E(B,G) is isomorphic to the first cohomology group of (A,B) with coefficients in G.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
L. Bemm, E.Z. Fornaroli, E.A. Jr.,