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arXiv · 2207.10713

Commutativity preservers of incidence algebras

Érica Z. Fornaroli·Mykola Khrypchenko·Ednei A. Santulo Jr
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Abstract

Let $I(X,K)$ be the incidence algebra of a finite connected poset $X$ over a field $K$ and $D(X,K)$ its subalgebra consisting of diagonal elements. We describe the bijective linear maps $\varphi:I(X,K)\to I(X,K)$ that strongly preserve the commutativity and satisfy $\varphi(D(X,K))=D(X,K)$. We prove that such a map $\varphi$ is a composition of a commutativity preserver of shift type and a commutativity preserver associated to a quadruple $(\theta,\sigma,c,\kappa)$ of simpler maps $\theta$, $\sigma$, $c$ and a sequence $\kappa$ of elements of $K$.

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Érica Z. Fornaroli, Mykola Khrypchenko, Ednei A. Santulo Jr. 2022-07-21. Commutativity preservers of incidence algebras. https://arxiv.org/abs/2207.10713

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