Matrices and Finite Biquandles

Sam Nelson; John Vo

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arXiv · math/0601145

Matrices and Finite Biquandles

Sam Nelson·John Vo

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Abstract

We describe a way of representing finite biquandles with n elements as 2n x 2n block matrices. Any finite biquandle defines an invariant of virtual knots through counting homomorphisms. The counting invariants of non-quandle biquandles can reveal information not present in the knot quandle, such as the non-triviality of the virtual trefoil and various Kishino knots. We also exhibit a virtual knot which is distinguished from its obverse and its reverse by a finite biquandle counting invariant. We classify biquandles of order 2, 3 and 4 and provide a URL for our Maple programs for computing with finite biquandles.

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BibTeX RIS

Sam Nelson, John Vo. 2006-04-18. Matrices and Finite Biquandles. https://arxiv.org/abs/math/0601145

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