Isomorphisms and derivations of partial flag incidence algebras

TL;DR

This paper characterizes the isomorphisms of partial flag incidence algebras over indecomposable rings as arising solely from poset isomorphisms and proves that all derivations are trivial, deepening understanding of their algebraic structure.

Contribution

It establishes a precise correspondence between algebraic isomorphisms and poset isomorphisms for partial flag incidence algebras and shows derivations are trivial.

Findings

Isomorphisms correspond to poset isomorphisms.

Derivations of the algebra are trivial.

Results hold for indecomposable rings.

Abstract

Let $P$ and $Q$ be finite posets and $R$ a commutative unital ring. In the case where $R$ is indecomposable, we prove that the $R$-linear isomorphisms between partial flag incidence algebras $I^3(P,R)$ and $I^3(Q,R)$ are exactly those induced by poset isomorphisms between $P$ and $Q$. We also show that the $R$-linear derivations of $I^3(P,R)$ are trivial.