Poisson Structures on Finitary Incidence Algebras

TL;DR

This paper provides a comprehensive classification of Poisson structures on finitary incidence algebras associated with any poset over a commutative ring, advancing the understanding of algebraic structures in combinatorics.

Contribution

It offers a complete description of Poisson structures on finitary incidence algebras for arbitrary posets, a novel result in algebraic combinatorics.

Findings

Full classification of Poisson structures on $FI(P,R)$

Applicable to any poset and commutative ring

Lays groundwork for further algebraic studies

Abstract

We give a full description of the Poisson structures on the finitary incidence algebra $FI(P,R)$ of an arbitrary poset $P$ over a commutative unital ring $R$.