The Classification Of Super Gel’ Fand-Dorfman Bialgebras In Small Dimensions

The super Gel’fand-Dorfman bialgebra is equivalent to the quadratic conformal superalgebra. They are closely related to the widely used Hamiltonian pairs, which plays fundamental roles in completely integrable systems. The research of super Gel’fand-Dorfman bialgebras ralated to vertex operator super algebra theory and play an important role in quantum field theory. And it is beneficial to the study of conformal field theory in physics.The main problem of algebra research are classification, represent and structure. In the sense of isomorphism, based on the classification of Novikov algebra in two-dimensional, we classify the Novikov superalgebra of three dimension. According to the results we have obtained and the basic definitions, we use the selection of optimization-based and method of undetermined coefficients to classify the super Gel’fand-Dorfman bialgebras of small dimensions.