2002/08/23 by Xiaoping Xu, Xu, Xiaoping · 1 citation
Mathematics · Physics and Astronomy · #17B69 #17D25 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:17B69 #msc:17D25
paper · pdf · doi:10.48550/arxiv.math/0208177
10pages
arxiv created 2002/08/23 · openalex publication_date 2002/08/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Novikov 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