Yazar "0000-0003-0925-8668" için listeleme
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Bicocycle double cross constructions
Esen, Oğul; Guha, Partha; Sütlü, Serkan (World Scientific, 2023-12-01)We introduce the notion of a bicocycle double cross product (sum) Lie group (algebra), and a bicocycle double cross product bialgebra, generalizing the unified products. On the level of Lie groups the construction yields ... -
Characteristic classes of foliations via SAYD-twisted cocycles
Rangipour, Bahram; Sütlü, Serkan Selçuk (European Mathematical Society, 2015)We find the first non trivial “SAYD-twisted” cyclic cocycle over the groupoid action algebra under the symmetry of the affine linear transformations of the Euclidian space. We apply the cocycle to construct a characteristic ... -
A characteristic map for compact quantum groups
Kaygun, Atabey; Sütlü, Serkan Selçuk (Springer Heidelberg, 2017-09)We 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 ... -
Cohomologies and generalized derivations of n-Lie algebras
Ateşli, Begüm; Esen, Oğul; Sütlü, Serkan (Electronic Journals Project, 2022)A cohomology theory associated to an n-Lie algebra and a representation space of it is introduced. It is shown that this cohomology theory classifies generalized derivations of n-Lie algebras as 1-cocycles, and inner ... -
Discrete dynamical systems over double cross-product Lie groupoids
Esen, Oğul; Sütlü, Serkan (World Scientific, 2021-03)Discrete Euler-Lagrange equations are studied over double cross product Lie groupoids. As such, a geometric framework for the local analysis of a discrete dynamical system is established. The arguments are elucidated on ... -
Epidemiyolojideki kompartman modellerinin eşlenmiş Hamilton analizi
Ateşli, Begüm; Esen, Oğul; Sütlü, Serkan (Marmara Üniversitesi Fen Bilimleri Enstitüsü, 2021-01-13)Epidemiyolojideki SIR, SEIR, 2-SIR ve 2-SEIR modellerinin Hamilton formülasyonu verildi. Eşlenmiş Lie-Poisson sistemleri yazıldı. SIR ve SEIR modellerinin eşlenmiş Lie-Poisson sistemi oldukları gösterildi. Bir Lie cebiri ... -
Eşlenmiş Lie grupları üzerindeki Lagrange fark denklemleri
Esen, Oğul; Kudeyt, Mahmut; Sütlü, Serkan (Marmara Üniversitesi Fen Bilimleri Enstitüsü, 2021-03-09)Bu makalede, kesikli (discrete) dinamiğin Lagrange formülasyonu eşlenmiş (matched pair) Lie grupları üzerinde çalışılmıştır. Sonuç olarak, karşılıklı etkileşim altındaki iki sistemin kolektif davranışını belirleyen eşlenmiş ... -
Hamiltonian dynamics on matched pairs
Sütlü, Serkan; Esen, Oğul (World Scientific Publishing Co, 2016-11-01)The cotangent bundle of a matched pair Lie group, and its trivialization, are shown to be a matched pair Lie group. The explicit matched pair decomposition on the trivialized bundle is presented. On the trivialized space, ... -
Hochschild cohomology of reduced incidence algebras
Sütlü, Serkan Selçuk; Kaygun, Atabey; Kanuni Er, Müge (World Scientific Publishing Co Pte Ltd, 2016-10-19)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 ... -
Hom-Lie-Hopf algebras
Halıcı, Serpil; Karataş, Adnan; Sütlü, Serkan Selçuk (Academic Press Inc., 2020-07-01)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 ... -
Homology of quantum linear groups
Kaygun, Atabey; Sütlü, Serkan (Int Press Boston, 2021-03-24)For every n >= 1, we calculate the Hochschild homology of the quantum monoids M-q(n), and the quantum groups GL(q)(n) and SLq(n) with coefficients in a 1-dimensional module coming from a modular pair in involution. -
Hopf-cyclic cohomology of quantum enveloping algebras
Kaygun, Atabey; Sütlü, Serkan Selçuk (European Mathematical Society Publishing House, 2016)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 ... -
Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebras with infinite dimensional coefficients
Rangipour, Bahram; Sütlü, Serkan Selçuk; Aliabadi, F. Yazdani (Springer Heidelberg, 2018-12-01)We 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 ... -
Hopf-dihedral (co)homology and L-theory
Kaygun, Atabey; Sütlü, Serkan Selçuk (European Mathematical Soc, 2018-03-23)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 dihedral Chern character to detect non-trivial ... -
Lagrangian dynamics on matched pairs
Sütlü, Serkan Selçuk; Esen, Oğul (Elsevier Science BV, 2017-01)Given 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 ... -
Lie cebiroidleri üzerindeki Lagrange dinamiğinin eşlenmesi problemi üzerine
Esen, Oğul; Kaya, Hanife Kübra; Sütlü, Serkan (Süleyman Demirel Üniversitesi, 2021-08-15)Lie cebiroidleri, bir anlamda tanjant demetini ve Lie cebiri yapısını beraber ihtiva eden ve fakat daha genel olan geometrik inşaalardır. Lagrange dinamiğinin en genel ifadesi Lie cebiroidleri üzerinde mümkündür. Bu makalede, ... -
Matched pair analysis of the Vlasov plasma
Esen, Oğul; Sütlü, Serkan (American Institute of Mathematical Sciences-AIMS, 2021-06)We present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of ... -
Matched pairs of m-invertible hopf quasigroups
Hassanzadeh, Mohammad; Sütlü, Serkan Selçuk (Institute of Mathematics, Academy of Sciences Moldova, 2020)The matched pair theory (of groups) is studied for a class of quasigroups; namely, the m-inverse property loops. The theory is upgraded to the Hopf level, and the m-invertible Hopf quasigroups are introduced. -
Matching of cocycle extensions for second tangent groups
Uçgun, Filiz Çağatay; Esen, Oğul; Sütlü, Serkan (American Institute of Physics Inc., 2022-11-07)We present the second-order tangent group of a Lie group as a cocycle extension of the first-order tangent group. We exhibit matching of the second-order tangent groups of two mutually interacting Lie groups. We examine ... -
On extensions, Lie-Poisson systems, and dissipation
Esen, Oğul; Özcan, Gökhan; Sütlü, Serkan (Heldermann Verlag, 2022-07-06)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, ...