Construction of Gel'fand-Dorfman Bialgebras from Classical R-Matrices

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dc.creatorXu, Xiaoping
dc.date2002-08-23
dc.date.accessioned2026-07-07T04:50:21Z
dc.date.available2026-07-07T04:50:21Z
dc.descriptionNovikov algebras are algebras whose associators are left-symmetric and right multiplication operators are mutually commutative. A Gel'fand-Dorfman bialgebra is a vector space with a Lie algebra structure and a Novikov algebra structure, satisfying a certain compatibility condition. Such a bialgebraic structure corresponds to a certain Hamiltonian pairs in integrable systems. In this article, we present a construction of Gel'fand-Dorfman bialgebras from certain classical R-matrices on Lie algebras. In particular, we construct such R-matrices from certain abelian subalgebras of Lie algebras. As a result, we show that there exist nontrivial Novikov algebra structures on any finite-dimensional nonzero Lie algebra over an algebraically closed field with characteristic 0 or $p>5$ such that they form a Gel'fand-Dorfman bialgebra
dc.description10pages
dc.identifierhttps://arxiv.org/abs/math/0208177
dc.identifierhttp://arxiv.org/abs/math/0208177
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64762
dc.subjectQuantum Algebra
dc.subject17D25;17B69
dc.titleConstruction of Gel'fand-Dorfman Bialgebras from Classical R-Matrices
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