Constructing biquandles

We define biquandle structures on a given quandle, and show that any biquandle is given by some biquandle structure on its underlying quandle. By determining when two biquandle structures yield isomorphic biquandles, we obtain a relationship between the automorphism group of a biquandle and the auto...

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Bibliographic Details
Published in:arXiv.org 2019-12
Main Author: Horvat, Eva
Format: Article
Language:English
Subjects:
Automorphisms
Chemical industry
Online Access:Get full text
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Summary:We define biquandle structures on a given quandle, and show that any biquandle is given by some biquandle structure on its underlying quandle. By determining when two biquandle structures yield isomorphic biquandles, we obtain a relationship between the automorphism group of a biquandle and the automorphism group of its underlying quandle. As an application, we determine the automorphism groups of Alexander and dihedral biquandles. We also discuss product biquandles and describe their automorphism groups.
ISSN:2331-8422
DOI:10.48550/arxiv.1810.03027