Hom-Gel'fand-Dorfman conformal superbialgebras

Abstract

Gel'fand Dorfman superbialgebra, which is both a Lie superalgebra and a (left) Novikov superalgebra with some compatibility condition, appears in the study of Hamiltonian pairs in completely integrable systems and a class of special Lie conformal superalgebras called quadratic Lie conformal superalgebras. In the present paper, we generalize this algebraic structure to the Hom-conformal case . We introduce first, Hom-Novikov conformal superalgebras and exihibit several properties. Then we introduce Hom-Gel'fand Dorfman superbialgebra and provide some construction results.