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Yayın Topological Hopf algebras and their Hopf-cyclic cohomology(Taylor and Francis, 2019-01-29) Rangipour, Bahram; Sütlü, Serkan SelçukA natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of coefficients (AYD modules) over a topological Lie algebra and those over its universal enveloping (Hopf) algebra are isomorphic. For topological Hopf algebras, the category of coefficients is identified with the representation category of a topological algebra called the anti-Drinfeld double. Finally, a topological van Est type isomorphism is detailed, connecting the Hopf-cyclic cohomology to the relative Lie algebra cohomology with respect to a maximal compact subalgebra.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 Hochschild cohomology of reduced incidence algebras(World Scientific Publishing Co Pte Ltd, 2016-10-19) Kanuni Er, Müge; Kaygun, Atabey; Sütlü, Serkan SelçukWe 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.
