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arXiv · 1110.6390

Coxeter-Chein Loops

Rieuwert J. Blok·Stephen Gagola III
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Abstract

In 1974 Orin Chein discovered a new family of Moufang loops which are now called Chein loops. Such a loop can be created from any group $W$ together with $\mathbb{Z}_2$ by a variation on a semi-direct product. We study these loops in the case where $W$ is a Coxeter group and show that it has what we call a Chein-Coxeter system, a small set of generators of order 2, together with a set of relations closely related to the Coxeter relations and Chein relations. As a result we are able to give amalgam presentations for Coxeter-Chein loops. This is to our knowledge the first such presentation for a Moufang loop.

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Rieuwert J. Blok, Stephen Gagola III. 2011-10-28. Coxeter-Chein Loops. https://arxiv.org/abs/1110.6390

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