2009/01/21 by Sacha C. Blumen, Blumen, Sacha C. · 1 citation
Mathematics · #17B37 #57M27 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:17B37 #msc:57M27
paper · pdf · doi:10.48550/arxiv.0901.3232
16 pages, 4 figures, accepted for publication by the Journal of Knot Theory and its Ramifications
arxiv created 2009/01/21 · openalex publication_date 2009/01/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let L be a link and ΦAL(q) its link invariant associated with the vector representation of the quantum (super)algebra Uq(A). Let FL(r,s) be the Kauffman link invariant for L associated with the Birman--Wenzl--Murakami algebra BWMf(r,s) for complex parameters r and s and a sufficiently large rank f. For an arbitrary link L, we show that Φosp(1|2n)L(q) = FL(-q2n,q) and Φso(2n+1)L(-q) = FL(q2n,-q) for each positive integer n and all sufficiently large f, and that Φosp(1|2n)L(q) and Φso(2n+1)L(-q) are identical up to a substitution of variables. For at least one class of links FL(-r,-s) = FL(r,s) implying Φosp(1|2n)L(q) = Φso(2n+1)L(-q) for these links.