On extensions, Lie-Poisson systems, and dissipation

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dc.authorid0000-0002-6766-0287
dc.authorid0000-0003-0925-8668
dc.contributor.authorEsen, Oğulen_US
dc.contributor.authorÖzcan, Gökhanen_US
dc.contributor.authorSütlü, Serkanen_US
dc.date.accessioned2022-09-01T13:32:45Z
dc.date.available2022-09-01T13:32:45Z
dc.date.issued2022-07-06
dc.departmentIşık Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümüen_US
dc.departmentIşık University, Faculty of Arts and Sciences, Department of Mathematicsen_US
dc.descriptionAcknowledgments. 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.en_US
dc.description.abstractLie-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.en_US
dc.description.versionPublisher's Versionen_US
dc.identifier.citationEsen, O. Özcan, G. & Sütlü, S. (2022). On extensions, Lie-Poisson systems, and dissipation. Journal Of Lie Theory, 32(2), 327-382.en_US
dc.identifier.endpage382
dc.identifier.issn0949-5932
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85136879502
dc.identifier.scopusqualityQ3
dc.identifier.startpage327
dc.identifier.urihttps://hdl.handle.net/11729/4812
dc.identifier.volume32
dc.identifier.wosWOS:000817805300003
dc.identifier.wosqualityQ4
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakScience Citation Index Expanded (SCI-EXPANDED)en_US
dc.institutionauthorSütlü, Serkanen_US
dc.institutionauthorid0000-0003-0925-8668
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.publisherHeldermann Verlagen_US
dc.relation.ispartofJournal Of Lie Theoryen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectLie-Poisson equationen_US
dc.subjectMetriplectic systemen_US
dc.subjectUnified producten_US
dc.subjectEuler-poincare equationsen_US
dc.subjectSemidirect productsen_US
dc.subjectBracket formulationen_US
dc.subjectDynamicsen_US
dc.subjectGeometryen_US
dc.subjectMomentsen_US
dc.subjectReductionen_US
dc.subjectAlgebraen_US
dc.subjectFluidsen_US
dc.subjectMagnetohydrodynamicsen_US
dc.subjectNoether's theoremen_US
dc.subjectLagrangianen_US
dc.titleOn extensions, Lie-Poisson systems, and dissipationen_US
dc.typeArticleen_US
dspace.entity.typePublication

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