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- W1631340674 abstract "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" @default.
- W1631340674 created "2016-06-24" @default.
- W1631340674 creator A5000876267 @default.
- W1631340674 date "2002-08-23" @default.
- W1631340674 modified "2023-09-27" @default.
- W1631340674 title "Construction of Gel'fand-Dorfman Bialgebras from Classical R-Matrices" @default.
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