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arXiv · 2606.02023

Variants of Coxeter quandles associated with Pin groups

Yuichi Kabaya
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Abstract

We study two families of quandles arising from Coxeter quandles. One is the quandle defined by Andruskiewitsch-Graña, which is the set of roots with binary operation defined by using the negatives of reflections. We observe that this is realized as a conjugation quandle in a Pin group. The other, which we call a rotational $D_n$ quandle, is the set of some right angle rotations in the Coxeter group of type $D_n$ with binary operation given by conjugation. We determine their inner automorphism groups, and observe that they are quite similar.

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Yuichi Kabaya. 2026-06-11. Variants of Coxeter quandles associated with Pin groups. https://arxiv.org/abs/2606.02023

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