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arXiv · 1708.02362

Subquandles of affine quandles

Přemysl Jedlička·Agata Pilitowska·David Stanovský·Anna Zamojska-Dzienio
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Abstract

A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their displacement group, by a universal algebraic condition coming from the commutator theory, and by an explicit construction over abelian groups. As a consequence, we obtain efficient algorithms for recognizing affine and quasi-affine quandles, and we enumerate small quasi-affine quandles. We also prove that the "abelian implies quasi-affine" problem of universal algebra has affirmative answer for the class of quandles.

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Přemysl Jedlička, Agata Pilitowska, David Stanovský, Anna Zamojska-Dzienio. 2017-08-08. Subquandles of affine quandles. https://arxiv.org/abs/1708.02362

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