Yazar "Kaygun, Atabey" seçeneğine göre listele

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    A characteristic map for compact quantum groups
    (Springer Heidelberg, 2017-09) Kaygun, Atabey; Sütlü, Serkan Selçuk
    We show that if G is a compact Lie group and g is its Lie algebra, then there is a map from the Hopf-cyclic cohomology of the quantum enveloping algebra U-q(g) to the twisted cyclic cohomology of quantum group algebra O(G(q)). We also show that the Schmudgen-Wagner index cocycle associated with the volume form of the differential calculus on the standard Podles sphere O(S-q(2)) is in the image of this map.
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    Hochschild cohomology of reduced incidence algebras
    (World Scientific Publishing Co Pte Ltd, 2016-10-19) Kanuni Er, Müge; Kaygun, Atabey; Sütlü, Serkan Selçuk
    We compute the continuous Hochschild cohomology of four reduced incidence algebras: the algebra of formal power series, the algebra of exponential power series, the algebra of Eulerian power series, and the algebra of formal Dirichlet series. We achieve the result by carrying out the computation for the coalgebra Cotor-groups of their pre-dual coalgebras.
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    Homology of quantum linear groups
    (Int Press Boston, 2021-03-24) Kaygun, Atabey; Sütlü, Serkan
    For every n >= 1, we calculate the Hochschild homology of the quantum monoids M-q(n), and the quantum groups GL(q)(n) and SLq(n) with coefficients in a 1-dimensional module coming from a modular pair in involution.
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    Hopf-cyclic cohomology of quantum enveloping algebras
    (European Mathematical Society Publishing House, 2016) Kaygun, Atabey; Sütlü, Serkan Selçuk
    In 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.
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    Hopf-dihedral (co)homology and L-theory
    (European Mathematical Soc, 2018-03-23) Kaygun, Atabey; Sütlü, Serkan Selçuk
    We 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.
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    On the Hochschild homology of smash biproducts
    (Elsevier B.V., 2021-02) Kaygun, Atabey; Sütlü, Serkan Selçuk
    We 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.