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Bölüm: Işık University, Faculty of Arts and Sciences, Department of Mathematics × Konu: Algebra ×

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Listeleniyor 1 - 7 / 7
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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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    Hom-Lie-Hopf algebras
    (Academic Press Inc., 2020-07-01) Halıcı, Serpil; Karataş, Adnan; Sütlü, Serkan Selçuk
    We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general (α,β)-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of (α,Id)-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras.
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    Topological Hopf algebras and their Hopf-cyclic cohomology
    (Taylor and Francis, 2019-01-29) Rangipour, Bahram; Sütlü, Serkan Selçuk
    A 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.
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    Complex travelling wave solutions to the KdV and Burgers equations
    (Elsevier Science Inc, 2005-03) Demiray, Hilmi
    In the present work, making use of the hyperbolic tangent method, some complex travelling wave solutions to the Korteweg-deVries and Burgers equations are obtained. It is observed that the real part of the Solution for the Burgers equation is of shock type whereas the imaginary part is the localized travelling wave. However, for the solution of the Korteweg-deVries equation the real part is a solitary wave while the imaginary part is the product of a solitary wave with a shock.
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    The modified reductive perturbation method as applied to Boussinesq equation: strongly dispersive case
    (Elsevier Science Inc, 2005-05-05) Demiray, Hilmi
    In this work, we extended the application of "the modified reductive perturbation method" to Boussinesq equation for strongly dispersive case and tried to obtain the contribution of higher order terms in the perturbation expansion. It is shown that the first order term in the perturbation expansion is governed by the non-linear Schrodinger equation and the second order term is governed by the linearized Schrodinger equation with a non-homogeneous term. In the long-wave limit, a travelling wave type of solution to these equations is also given.
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    Graphs of given order and size and minimum algebraic connectivity
    (Elsevier Science Inc, 2012-04-01) Bıyıkoğlu, Türker; Leydold, Josef
    The structure of connected graphs of given size and order that have minimal algebraic connectivity is investigated. It is shown that they must consist of a chain of cliques. Moreover, an upper bound for the number of maximal cliques of size 2 or larger is derived.
  • Küçük Resim Yok
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    On extensions, Lie-Poisson systems, and dissipation
    (Heldermann Verlag, 2022-07-06) Esen, Oğul; Özcan, Gökhan; Sütlü, Serkan
    Lie-Poisson systems on the dual spaces of unified products are studied. Having been equipped with a twisted 2-cocycle term, the extending structure framework allows not only to study the dynamics on 2-cocycle extensions, but also to (de)couple mutually interacting Lie-Poisson systems. On the other hand, symmetric brackets; such as the double bracket, the Cartan-Killing bracket, the Casimir dissipation bracket, and the Hamilton dissipation bracket are worked out in detail. Accordingly, the collective motion of two mutually interacting irreversible dynamics, as well as the mutually interacting metriplectic flows, are obtained. The theoretical results are illustrated in three examples. As an infinite-dimensional physical model, decompositions of the BBGKY hierarchy are presented. As for the finite-dimensional examples, the coupling of two Heisenberg algebras, and the coupling of two copies of 3D dynamics are studied.