5 sonuçlar
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Yayın Characteristic classes of foliations via SAYD-twisted cocycles(European Mathematical Society, 2015) Rangipour, Bahram; Sütlü, Serkan SelçukWe find the first non trivial “SAYD-twisted” cyclic cocycle over the groupoid action algebra under the symmetry of the affine linear transformations of the Euclidian space. We apply the cocycle to construct a characteristic map by which we transfer the characteristic classes of transversely orientable foliations into the cyclic cohomology of the groupoid action algebra. In codimension 1, our result matches with the (only explicit) computation done by Connes–Moscovici. We carry out the explicit computation in codimension 2 to present the transverse fundamental class, the Godbillon–Vey class, and the other four residual classes as cyclic cocycles on the groupoid action algebra.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 Hom-Lie-Hopf algebras(Academic Press Inc., 2020-07-01) Halıcı, Serpil; Karataş, Adnan; Sütlü, Serkan SelçukWe studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general (α,β)-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of (α,Id)-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras.Yayın On the Hochschild homology of smash biproducts(Elsevier B.V., 2021-02) Kaygun, Atabey; Sütlü, Serkan SelçukWe develop a new spectral sequence in order to calculate the Hochschild homology of smash biproducts (also called the twisted tensor products) of unital associative algebras A#B provided one of A or B has Hochschild dimension less than 2. We use this spectral sequence to calculate Hochschild homology of the algebra Mq(2) of quantum 2×2-matrices.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.
