From biquandle structures to Hom-biquandles

Alissa S. Crans; Eva Horvat

From biquandle structures to Hom-biquandles

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arxiv 1907.10259 v1 pith:CI34LJCX submitted 2019-07-24 math.GT math.GR

Eva Horvat , Alissa S. Crans This is my paper · ORCID

classification math.GTmath.GR

keywords biquandlecoloringhom-biquandlequandlerelationshipstructuresanalogsauthor

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We investigate the relationship between the quandle and biquandle coloring invariant and obtain an enhancement of the quandle and biquandle coloring invariants using biquandle structures. We also continue the study of biquandle homomorphisms into a medial biquandle begun by the second author et al., finding biquandle analogs of results about Hom-quandles. We describe the biquandle structure of the Hom-biquandle, and consider the relationship between the Hom-quandle and Hom-biquandle.

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General constructions of biquandles and their symmetries
math.GR 2019-08 conditional novelty 7.0 of 10

All word pairs over two free generators that make every group a birack or biquandle are classified, and new union, product, holomorph, and covering constructions for biquandles are introduced with their automorphism groups.

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