Singular Hecke algebras, Markov traces, and HOMFLY-type invariants

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dc.creatorParis, Luis
dc.creatorRabenda, Loic
dc.date2007-07-03
dc.date.accessioned2026-07-07T08:13:45Z
dc.date.available2026-07-07T08:13:45Z
dc.descriptionWe define the singular Hecke algebra ${\mathcal H} (SB_n)$ as the quotient of the singular braid monoid algebra ${\mathbb C} (q) [SB_n]$ by the Hecke relations $σ_k^2 = (q-1) σ_k +q$, $1 \le k\le n-1$, and define the Markov traces on the sequence $\{{\mathcal H}(SB_n)\}_{n=1}^{+\infty}$ 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.
dc.identifierhttps://arxiv.org/abs/0707.0400
dc.identifierhttp://arxiv.org/abs/0707.0400
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132877
dc.subjectGeometric Topology
dc.subjectRepresentation Theory
dc.subject57M25
dc.titleSingular Hecke algebras, Markov traces, and HOMFLY-type invariants
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