Group gradings on finite dimensional incidence algebras

Ednei A. Santulo; Jonathan P. Souza; Felipe Y. Yasumura

doi:10.1016/j.jalgebra.2019.10.026

paper

Group gradings on finite dimensional incidence algebras

arXiv:1905.08391 · doi:10.1016/j.jalgebra.2019.10.026

Abstract

In this work, we classify the group gradings on finite-dimensional incidence algebras over a field, where the field has characteristic zero, or the characteristic is greater than the dimension of the algebra, or the grading group is abelian. Moreover, we investigate the structure of $G$ -graded $(D_{1}, D_{2})$ -bimodules, where $G$ is an abelian group, and $D_{1}$ and $D_{2}$ are the group algebra of finite subgroups of $G$ . As a consequence, we can provide a more profound structure result concerning the group gradings on the incidence algebras, and we can classify their isomorphism classes of group gradings.

References in corpus (1)

Co-stability of radicals and its applications to PI-theory