Year: 2026
Type: preprint
Abstract: We study the behavior of good involutions under two fundamental constructions of quandles: interaction-free unions and direct products. In particular, we show that the set of good involutions on a quandle decomposes naturally into the set of involutions on its maximal trivial component and the set of good involutions on the complement. Moreover, we construct an example of a connected noninvolutory symmetric quandle with multiple good involutions, which serves as a counterexample to a conjecture by Ta.
Source: arXiv (Cornell University)
Authors: Nakajima, Yasuhito, Yamaguchi, Kentaro
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203919082