Flat Pencils of Symplectic Connections and Hamiltonian Operators of Degree 2
arXiv:0704.1401 · doi:10.1016/j.geomphys.2007.12.002
Abstract
Bi-Hamiltonian structures involving Hamiltonian operators of degree 2 are studied. Firstly, pairs of degree 2 operators are considered in terms of an algebra structure on the space of 1-forms, related to so-called Fermionic Novikov algebras. Then, degree 2 operators are considered as deformations of hydrodynamic type Poisson brackets.
20 pages