Vladimir Mangazeev ( Australian National University, Canberra): On braided Hopf structures on exterior algebras

The second lecture of the mini-course "On braided Hopf structures on exterior algebras"

Abstract: We show that the exterior algebra of a vector space V of dimension greater than one admits a one-parameter family of braided Hopf algebra structures. We explicitly compute the structure constants with respect to a natural set-theoretic basis. A one-parameter family of diagonal automorphisms exists, which we use to construct solutions to the (constant) Yang--Baxter equation. These solutions are conjectured to give rise to the two-variable Links--Gould polynomial invariants associated with the super-quantum group Uq(gl(N|1)), where N=dim(V).