Gradings on incidence algebras and their graded polynomial identities

摘要

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 in-equivalent elementary G-gradings on this algebra. If P is bounded, F is an infinite field of characteristic zero, and A, B are both elementary G-graded incidence algebras of P satisfying the same G-graded polynomial identities, and the automorphism group of P acts transitively on the maximal chains of P, we show that A and B are graded isomorphic.