2007/07/03 by Luis Paris, Paris, Luis, Loïc Rabenda +1
Mathematics · #57M25 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.0707.0400
openalex publication_date 2007/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the singular Hecke algebra \mathcal H (SBn) as the quotient of the singular braid monoid algebra \mathbb C (q) [SBn] by the Hecke relations σk2 = (q-1) σk +q, 1 ≤ k≤ n-1, and define the Markov traces on the sequence \\mathcal H(SBn)\n=1+∞ in the same way as for the Markov traces on the tower of (non-singular) Hecke algebras of the symmetric groups. We prove that the Markov traces are in one-to-one correspondance with the invariants that satisfies some skein relation, and compute an explicit classification of the Markov traces. Thanks to this classification, we define some universal HOMFLY-type invariant which has the property that it distinguishes all the pairs of singular links that can be distinguished by an invariant which satisfies the required skein relation.