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arXiv · 2306.12512

Involutions of the second kind on finitary incidence algebras

Érica Zancanella Fornaroli
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Abstract

Let $K$ be a field and $X$ a connected partially ordered set. In the first part of this paper, we show that the finitary incidence algebra $FI(X,K)$ of $X$ over $K$ has an involution of the second kind if and only if $X$ has an involution and $K$ has an automorphism of order $2$. We also give a characterization of the involutions of the second kind on $FI(X,K)$. In the second part, we give necessary and sufficient conditions for two involutions of the second kind on $FI(X,K)$ to be equivalent in the case where $char K\neq 2$ and every multiplicative automorphism of $FI(X,K)$ is inner.

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Érica Zancanella Fornaroli. 2023-06-21. Involutions of the second kind on finitary incidence algebras. https://arxiv.org/abs/2306.12512

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