Hopf-cyclic cohomology of quantum enveloping algebras (Q740097)

Summary: In this paper we calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra \(U_q(\mathfrak{g})\) for an arbitrary semi-simple Lie algebra \(\mathfrak{g}\) with coefficients in a modular pair in involution. We obtain this result by showing that the coalgebra Hochschild cohomology of these Hopf algebras are concentrated in a single degree determined by the rank of the Lie algebra \(\mathfrak{g}\).