Quantum link invariant from the Lie superalgebra ${\mathfrak D}_{2 1,\alpha}$

Abstract

The usual construction of link invariants from quantum groups applied to the superalgebra ${\mathfrak{D}}_{21,\alpha }$ 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).