Quantum enveloping superalgebras and link invariants

Abstract

Corresponding to each finite dimensional simple basic classical Lie superalgebra, a new quantum enveloping superalgebra is introduced, which has the structure of a braided quasi-Hopf superalgebra. In the case of osp(1|2n), this quantum enveloping superalgebra is shown to be isomorphic to the standard Drinfeld–Jimbo quantum superalgebra Uq(osp(1|2n)) as braided quasi Hopf superalgebras. The new quantum enveloping superalgebras are applied to construct link invariants, from which Vassiliev invariants can be readily extracted. This, in particular, provides a useful construction for the Vassiliev invariants associated with Uq(osp(1|2n)).