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

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

2002-08-23

arxiv.org/abs/math/0208177v1

Mathematics

Quantum Algebra

10pages

Scientific paper

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

Affiliated with

Also associated with

No associations

Rating

Construction of Gel'fand-Dorfman Bialgebras from Classical R-Matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Construction of Gel'fand-Dorfman Bialgebras from Classical R-Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Construction of Gel'fand-Dorfman Bialgebras from Classical R-Matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-95010