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Yayın Hamiltonian dynamics on matched pairs(World Scientific Publishing Co, 2016-11-01) Esen, Oğul; Sütlü, SerkanThe 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, the canonical symplectic two-form and the canonical Poisson bracket are explicitly written. Various symplectic and Poisson reductions are perfomed. The Lie–Poisson bracket is derived. As an example, Lie–Poisson equations on (Formula presented.) are obtained.Yayın Bicocycle double cross constructions(World Scientific, 2023-12-01) Esen, Oğul; Guha, Partha; Sütlü, SerkanWe 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 a Lie group on the product space of two pointed manifolds, none of which being necessarily a subgroup. On the level of Lie algebras, a Lie algebra is obtained on the direct sum of two vector spaces, which are not required to be subalgebras. Finally, on the quantum level a bialgebra is obtained on the tensor product of two (co)algebras that are not necessarily sub-bialgebras.Yayın Discrete dynamical systems over double cross-product Lie groupoids(World Scientific, 2021-03) Esen, Oğul; Sütlü, SerkanDiscrete 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 the local discrete dynamics of a gauge groupoid. The discrete Elroy's beanie is studied as a physical example.Yayın Matching of cocycle extensions for second tangent groups(American Institute of Physics Inc., 2022-11-07) Uçgun, Filiz Çağatay; Esen, Oğul; Sütlü, SerkanWe 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 the cocycle extension character of the matched second-order group and arrive at that matched pair of cocycle extensions is a cocycle extension by itself.
