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arXiv · 2401.17964

Multiplicative Automorphisms of Incidence Algebras

Evgenii Kaigorodov·Piotr Krylov·Askar Tuganbaev
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Abstract

Let $I(X,R)$ be the incidence algebra of the preordered set $X$ over the ring $R$. In the case of a finite connected partially ordered set $X$, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group of multiplicative automorphisms of the algebra $I(X,R)$. As a consequence, we obtain several matching criteria of the subgroup of inner multiplicative automorphisms with the group of multiplicative automorphisms.

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Evgenii Kaigorodov, Piotr Krylov, Askar Tuganbaev. 2024-01-31. Multiplicative Automorphisms of Incidence Algebras. https://arxiv.org/abs/2401.17964

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