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arXiv · 1412.3693

Construction of a two unique product semigroup defined by permutation relations of quaternion type

Ferran Cedo·Eric Jespers·Georg Klein
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Abstract

For a regular representation $H \subseteq \text{Sym}_n$ of the generalized quaternion group of order $n=4k$, with $k\geq 2$, the monoid $S_n(H)$ presented with generators $a_1,a_2,\dots ,a_n$ and with relations $a_1a_2\cdots a_n=a_{\sigma(1)}a_{\sigma(2)}\cdots a_{\sigma(n)}$, for all $\sigma\in H$, is investigated. It is shown that $S_n(H)$ has the two unique product property. As a consequence, for any field $K$, the monoid algebra $K[S_n(H)]$ is a domain with trivial units which is semiprimitive.

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Ferran Cedo, Eric Jespers, Georg Klein. 2014-12-11. Construction of a two unique product semigroup defined by permutation relations of quaternion type. https://doi.org/10.1016/j.jalgebra.2015.12.017

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