2025/01/29 by Jorge Becerra, Becerra, Jorge · 3 citations
Mathematics · #16T05 #18M10 #18M15 #57K10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2501.17668
openalex publication_date 2025/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The universal invariant with respect to a given ribbon Hopf algebra is a tangle invariant that dominates all the Reshetikhin-Turaev invariants built from the representation theory of the algebra. We construct a canonical strict monoidal functor that encodes the universal invariant of upwards tangles and refines the Kerler-Kauffman-Radford functorial invariant. Moreover, this functor preserves the braiding, twist and the open trace, the latter being a mild modification of Joyal-Street-Verity's notion of trace in a balanced category. We construct this functor using the more flexible XC-algebras, a class which contains both ribbon Hopf algebras and endomorphism algebras of representation of these.