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arXiv · 2307.08439

Skew derivations of incidence algebras

Érica Z. Fornaroli·Mykola Khrypchenko
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Abstract

In the first part of the paper we describe $\varphi$-derivations of the incidence algebra $I(X,K)$ of a locally finite poset $X$ over a field $K$, where $\varphi$ is an arbitrary automorphism of $I(X,K)$. We show that they admit decompositions similar to that of usual derivations of $I(X,K)$. In particular, the quotient of the space of $\varphi$-derivations of $I(X,K)$ by the subspace of inner $\varphi$-derivations of $I(X,K)$ is isomorphic to the first group of certain cohomology of $X$, which is developed in the second part of the paper.

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Érica Z. Fornaroli, Mykola Khrypchenko. 2023-07-17. Skew derivations of incidence algebras. https://arxiv.org/abs/2307.08439

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