Browsing by Author "Kaygun, Atabey"
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A characteristic map for compact quantum groups
Kaygun, Atabey; Sütlü, Serkan Selçuk (Springer Heidelberg, 201709)We show that if G is a compact Lie group and g is its Lie algebra, then there is a map from the Hopfcyclic cohomology of the quantum enveloping algebra Uq(g) to the twisted cyclic cohomology of quantum group algebra ... 
Hochschild cohomology of reduced incidence algebras
Sütlü, Serkan Selçuk; Kaygun, Atabey; Kanuni Er, Müge (World Scientific Publishing Co Pte Ltd, 20161019)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 ... 
Homology of quantum linear groups
Kaygun, Atabey; Sütlü, Serkan (Int Press Boston, 2021)For every n >= 1, we calculate the Hochschild homology of the quantum monoids Mq(n), and the quantum groups GL(q)(n) and SLq(n) with coefficients in a 1dimensional module coming from a modular pair in involution. 
Hopfcyclic cohomology of quantum enveloping algebras
Kaygun, Atabey; Sütlü, Serkan Selçuk (European Mathematical Society Publishing House, 2016)In this paperwe calculate both the periodic and nonperiodic Hopfcyclic cohomology of DrinfeldJimbo quantum enveloping algebra Uq.g/ for an arbitrary semisimple Lie algebra g with coefficients in a modular pair in ... 
Hopfdihedral (co)homology and Ltheory
Kaygun, Atabey; Sütlü, Serkan Selçuk (European Mathematical Soc, 20180323)We develop an appropriate dihedral extension of the ConnesMoscovici characteristic map for Hopf *algebras. We then observe that one can use this extension together with the dihedral Chern character to detect nontrivial ... 
On the Hochschild homology of smash biproducts
Kaygun, Atabey; Sütlü, Serkan Selçuk (Elsevier B.V., 202102)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 ...