On extensions, Lie-Poisson systems, and dissipation

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Tarih

2022-07-06

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Heldermann Verlag

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Araştırma projeleri

Organizasyon Birimleri

Dergi sayısı

Özet

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.

Açıklama

Acknowledgments. This paper is a part of the project “Matched pairs of Lagrangian and Hamiltonian Systems” supported by TÜBİTAK (the Scientific and Technological Research Council of Turkey) with the project number 117F426, the support of which is acknowledged by the authors.

Anahtar Kelimeler

Lie-Poisson equation, Metriplectic system, Unified product, Euler-poincare equations, Semidirect products, Bracket formulation, Dynamics, Geometry, Moments, Reduction, Algebra, Fluids, Magnetohydrodynamics, Noether's theorem, Lagrangian

Kaynak

Journal Of Lie Theory

WoS Q Değeri

Q4
Q4

Scopus Q Değeri

Q3

Cilt

32

Sayı

2

Künye

Esen, O., Özcan, G.& Sütlü, S. (2022). On extensions, Lie-Poisson systems, and dissipation. Journal Of Lie Theory, 32(2), 327-382.