Gradings on Incidence Algebras and their Graded Polynomial Identities
Rings and Algebras
2021-02-03 v1
Abstract
Let P a locally finite partially ordered set, F a field, G a group, and I(P,F) the incidence algebra of P over F. We describe all the inequivalent elementary G-gradings on this algebra. If P is bounded, F is a infinite field of characteristic zero, and A, B are both elementary G-graded incidence algebras satisfying the same G-graded polynomial identities, and the automorphisms group of P acts transitively on the maximal chains of P , we show that A and B are graded isomorphic.
Keywords
Cite
@article{arxiv.2004.05230,
title = {Gradings on Incidence Algebras and their Graded Polynomial Identities},
author = {Humberto Luiz Talpo and Waldeck Schützer},
journal= {arXiv preprint arXiv:2004.05230},
year = {2021}
}
Comments
10 pages, 1 figure