JOURNAL OF NONCOMMUTATIVE GEOMETRY, cilt.10, sa.2, ss.429-446, 2016 (SCI-Expanded)
In this paper we calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra U-q (g) for an arbitrary semi-simple Lie algebra 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 g.