Knot invariants from XC-structures on the Sweedler algebra are trivial

Jorge Becerra

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arXiv · 2601.19840

Knot invariants from XC-structures on the Sweedler algebra are trivial

Jorge Becerra

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Abstract

An XC-algebra is the minimum algebraic structure needed to define a framed, oriented knot invariant and generalises Lawrence's invariant obtained from ribbon Hopf algebras. In this note, we show that the knot invariant produced by any XC-structure on the Sweedler algebra is completely determined by the framing of the knot. Furthermore, we also exhibit explicit families of XC-structures on the Sweedler algebra that do not have a ribbon Hopf-algebraic origin.

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Jorge Becerra. 2026-01-27. Knot invariants from XC-structures on the Sweedler algebra are trivial. https://arxiv.org/abs/2601.19840

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