The knot invariant associated to two-parameter quantum algebras

2022/03/20 by Fan Zhaobing, Fan, Zhaobing, Xing Junjing +1
Mathematics · Physics and Astronomy · #17B37 #18M15 #57K14 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2203.10478

openalex publication_date 2022/03/20 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Using the skew-Hopf pairing, we obtain R-matrix for the two-parameter quantum algebra U_v,t. We further construct a strict monoidal functor T from the tangle category (OTa,⊗, ∅) to the category (Mod,⊗, ℚ(v,t)) of U_v,t-modules . As a consequence, the quantum knot invariant of the tangle L of type (n,n) is obtained by the action of T on the closure L of L.

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