Knot invariants from XC-structures on the Sweedler algebra are trivial
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911402938073088 |
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| author | Becerra, Jorge |
| author_facet | Becerra, Jorge |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19840 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Knot invariants from XC-structures on the Sweedler algebra are trivial Becerra, Jorge Geometric Topology Quantum Algebra 16T05, 16T30, 18M15, 57K10, 57K16 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. |
| title | Knot invariants from XC-structures on the Sweedler algebra are trivial |
| topic | Geometric Topology Quantum Algebra 16T05, 16T30, 18M15, 57K10, 57K16 |
| url | https://arxiv.org/abs/2601.19840 |