Isomorphisms and derivations of partial flag incidence algebras

Abstract

Let [Formula: see text] and [Formula: see text] be finite posets and [Formula: see text] a commutative unital ring. In the case where [Formula: see text] is indecomposable, we prove that the [Formula: see text]-linear isomorphisms between partial flag incidence algebras [Formula: see text] and [Formula: see text] are exactly those induced by poset isomorphisms between [Formula: see text] and [Formula: see text]. We also show that the [Formula: see text]-linear derivations of [Formula: see text] are trivial.