XC-algebras and quantum knot invariants (Jorge Becerra, Dijon)

28.05.2026 14:15

Ribbon Hopf algebras and their representations allow to construct quantum knot invariants that recover classical invariants like the Alexander or Jones polynomial. In this talk I would like to introduce the minimal algebraic structure needed to define a knot invariant à la Lawrence, the so-called XC-algebras. This framework encodes the invariants produced both with ribbon Hopf algebras and their representation theory, but it is much more general. Yet, the invariant produced with a XC-algebra gives rise to a monoidal functor that extends the celebrated Reshetikhin-Turaev functor. Lastly, I will explain how this story canonically generalises to a virtual knot and tangle quantum invariant.

Lieu

Bâtiment: Conseil Général 7-9

Seminar room, 8th floor, Séminaire "Topologie et
géométrie"

entrée libre