Group gradings on finite dimensional incidence algebras

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.