Communications of the
Korean Mathematical Society CKMS

We use the structure of skew braces to enhance the biquandle counting invariant for virtual knots and links for finite biquandles defined from skew braces. We introduce two new invariants: a single-variable polynomial using skew brace ideals and a two-variable polynomial using the skew brace group structures. We provide examples to show that the new invariants are not determined by the counting invariant and hence are proper enhancements.

Keywords: Skew braces, biquandles, enhancements of counting invariants, virtual knots

MSC numbers: 57K12

Supported by: The second author was partially supported by Simons Foundation Collaboration Grant 702597.