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Yayın Hopf-cyclic cohomology of quantum enveloping algebras(European Mathematical Society Publishing House, 2016) Kaygun, Atabey; Sütlü, Serkan SelçukIn this paperwe calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra Uq.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.Yayın Hopf-dihedral (co)homology and L-theory(European Mathematical Soc, 2018-03-23) Kaygun, Atabey; Sütlü, Serkan SelçukWe develop an appropriate dihedral extension of the Connes-Moscovici characteristic map for Hopf *-algebras. We then observe that one can use this extension together with the dihedral Chern character to detect non-trivial L-theory classes of a *-algebra that carry a Hopf symmetry over a Hopf *-algebra. Using our machinery we detect a previously unknown L-class of the standard Podles sphere.
