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arXiv · 2506.14216

Associative Pentagon Algebras

Marzia Mazzotta·Agata Pilitowska
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Abstract

A set-theoretic solution to the Pentagon Equation can be described as a \emph{pentagon} algebra $(S, \cdot, \ast)$ such that $(S, \cdot)$ is a semigroup and the operations $\cdot$ and $\ast$ are related by two additional equations. This paper aims to investigate associative pentagon algebras in which $(S, \ast)$ is also a semigroup. We introduce and describe two families of associative pentagon algebras which are strongly determined by the properties of the semigroup $(S,\ast)$. We present a complete characterization of such algebras using semigroup equations. We also provide constructions of such associative pentagon algebras and give several classes of examples.

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Marzia Mazzotta, Agata Pilitowska. 2025-06-17. Associative Pentagon Algebras. https://arxiv.org/abs/2506.14216

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