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Hopf-cyclic Cohomology of Quantum Enveloping Algebras (1409.4002v1)
Published 14 Sep 2014 in math.KT and math.QA
Abstract: 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 show that its Hochschild cohomology is concentrated in a single degree determined by the rank of the Lie algebra $\mathfrak{g}$.