Automorphisms and antiautomorphisms of quandles

Abstract

In this paper we provide the conditions under which an automorphism or an antiautomorphism of a group $G$ induces an automorphism or an antiautomorphism of the $m$-conjugation quandle $\mathrm{Con}{\mathrm{j}}_{\mathrm{m}}(G),m\in \mathbb{Z}$, the core quandle $\mathrm{Core}(G)$, the generalized Alexander quandle $\mathrm{Alex}(G,\varphi )$ where $\varphi \in \mathrm{Aut}(G)$ and some others. We also construct automorphisms of these quandles that do not originate from $G$.