51 citations · 96 across the 34 of their papers we have counts for
19 papers · 1 filter
Birational Equivalences and Generalized Weyl Algebras
Atabey Kaygun
We calculate suitably localized Hochschild homologies of various quantum groups and Podleś spheres after realizing them as generalized Weyl algebras (GWAs). We use the fact that ev…
Homology of quantum linear groups
Atabey Kaygun, Serkan Sütlü
For every , we calculate the Hochschild homology of the quantum monoids , and the quantum groups and with coefficients in a 1-dimensional modul…
On the Hochschild homology of smash biproducts
Atabey Kaygun, Serkan Sütlü
We develop a new spectral sequence in order to calculate Hochschild homology of smash biproducts (also called twisted tensor products) of unital associative algebras provid…
Noncommutative Fibrations
Atabey Kaygun
We show that faithfully flat smooth extensions are reduced flat, and therefore, fit into the Jacobi-Zariski exact sequence in Hochschild homology and cyclic (co)homology even when…
The asymptotic Connes-Moscovici characteristic map and the index cocycles
Atabey Kaygun, Serkan Sütlü
We show that the (even and odd) index cocycles for theta-summable Fredholm modules are in the image of the Connes-Moscovici characteristic map. To show this, we first define a new…
Hochschild Cohomology of Reduced Incidence Algebras
Müge Kanuni, Atabey Kaygun, Serkan Sütlü
We compute the Hochschild cohomology of the reduced incidence algebras such as the algebra of formal power series, the algebra of exponential power series, the algebra of Eulerian…
Hopf-dihedral (co)homology and -theory
A. Kaygun, S. Sütlü
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 dihed…
Hopf-cyclic Cohomology of Quantum Enveloping Algebras
Atabey Kaygun, Serkan Sütlü
In this paper we calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra for an arbitrary semi-simple L…
The Weak Finitistic Dimension of a Path Algebra is Finite
Muge Kanuni, Atabey Kaygun
We prove a version of Bass' finitistic dimension conjecture for path algebras over arbitrary directed graphs. It is known that the path algebra of a finite directed graph is heredi…
Jacobi-Zariski Exact Sequence for Hochschild Homology and Cyclic (Co)Homology
Atabey Kaygun
We prove that for an inclusion of unital associative but not necessarily commutative algebras we have long exact sequences in Hochschild homology and cyclic (co)homo…
Uniqueness of pairings in Hopf-cyclic cohomology
Atabey Kaygun
We show that all pairings defined in the literature extending Connes-Moscovici characteristic map in Hopf-cyclic cohomology are isomorphic as natural transformations of derived dou…
Products in Hopf-Cyclic Cohomology
Atabey Kaygun
We construct several pairings in Hopf-cyclic cohomology of (co)module (co)algebras with arbitrary coefficients. The key ideas instrumental in constructing these pairings are the de…
The universal Hopf cyclic theory
Atabey Kaygun
We define a Hopf cyclic (co)homology theory in an arbitrary symmetric strict monoidal category. Thus we unify all different types of Hopf cyclic (co)homologies under one single uni…
Bivariant Hopf cyclic cohomology
Atabey Kaygun, Masoud Khalkhali
For module algebras and module coalgebras over an arbitrary bialgebra, we define two types of bivariant cyclic cohomology groups called bivariant Hopf cyclic cohomology and bivaria…
Hopf--Hochschild (co)homology of module algebras
Atabey Kaygun
We define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called module algebras. We show this (co)homo…
Excision in Hopf cyclic homology
Atabey Kaygun, Masoud Khalkhali
In this paper we show that both variants of the Hopf cyclic homology has excision under some natural homological conditions on the objects and the coefficient module.
Loday--Quillen--Tsygan Theorem for Coalgebras
Atabey Kaygun
In this paper we prove that Loday--Quillen--Tsygan Theorem generalizes to the case of coalgebras. Specifically, we show that the Chevalley--Eilenberg--Lie homology of the Lie coalg…
Bialgebra Cyclic Homology with Coefficients, Part II
Atabey Kaygun
This is the second part of the article [math.KT/0408094]. In the first paper, we used the underlying coalgebra structure to develop a cyclic theory. In this paper we define a dual…
Bialgebra Cyclic Homology with Coefficients, Part I
Atabey Kaygun
The cyclic (co)homology of Hopf algebras is defined by Connes and Moscovici [math.DG/9806109] and later extended by Khalkhali et.al [math.KT/0306288] to admit stable anti-Yetter-Dr…