6 sonuçlar
Arama Sonuçları
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Yayın A characteristic map for compact quantum groups(Springer Heidelberg, 2017-09) Kaygun, Atabey; Sütlü, Serkan SelçukWe 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.Yayın Second order Lagrangian dynamics on double cross product groups(Elsevier B.V., 2021-02) Oğul, Esen; Kudeyt, Mahmut; Sütlü, Serkan SelçukWe observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Based on this observation, we derive the 2nd order Euler–Lagrange equations on the 2nd order tangent group from the 1st order Euler–Lagrange equations on the iterated tangent group. We also present in detail the 2nd order Lagrangian dynamics on the 2nd order tangent group of a double cross product group.Yayın Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebras with infinite dimensional coefficients(Springer Heidelberg, 2018-12-01) Rangipour, Bahram; Sütlü, Serkan Selçuk; Aliabadi, F. YazdaniWe discuss a new strategy for the computation of the Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebra Hn. More precisely, we introduce a multiplicative structure on the Hopf-cyclic complex of Hn, and we show that the van Est type characteristic homomorphism from the Hopf-cyclic complex of Hn to the Gelfand-Fuks cohomology of the Lie algebra Wn of formal vector fields on Rn respects this multiplicative structure. We then illustrate the machinery for n = 1.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 Lagrangian dynamics on matched pairs(Elsevier Science BV, 2017-01) Sütlü, Serkan Selçuk; Esen, OğulGiven a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the Euler–Lagrange equations on the trivialized matched pair of tangent groups, as well as the Euler–Poincaré equations on the matched pair of Lie algebras. We show explicitly how these equations cover those of the semi-direct product theory. In particular, we study the trivialized, and the reduced Lagrangian dynamics on the group SL(2,C).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.
