Quantum link invariant from the Lie superalgebra D(2,1,alpha)

Details Quantum link invariant from the Lie superalgebra D(2,1,alpha) Quantum link invariant from the Lie superalgebra D(2,1,alpha)

2004-04-30

arxiv.org/abs/math/0404548v2

Algebr. Geom. Topol. 6 (2006) 329-349

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 12 March 2006

Scientific paper

10.2140/agt.2006.6.329

The usual construction of link invariants from quantum groups applied to the superalgebra D_{2 1,alpha} is shown to be trivial. One can modify this construction to get a two variable invariant. Unusually, this invariant is additive with respect to connected sum or disjoint union. This invariant contains an infinity of Vassiliev invariants that are not seen by the quantum invariants coming from Lie algebras (so neither by the colored HOMFLY-PT nor by the colored Kauffman polynomials).

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