The Classification Of Nontrivial Super Gel’fand-Dorfman Bialgebras In Four Dimensions

In this thesis, the definition of nontrivial super Gel’fand-Dorfman bialgebrasis given. According to the classification in3-dimensional case, we discuss the clas-sification of4-dimensional Novikov superalgebras. Then we get the results of theclassification of4-dimensional nontrivial super Gel’fand-Dorfman bialgebras by themethod of undetermined coefcients and optimization. In order to get all the pos-sible of super Gel’fand-Dorfman bialgebras, we need to make the transformation ofbase. We get main conclusions about4-dimensional super Gel’fand-Dorfman bial-gebras as follows:1. Let （A,[,],o） be a super Gel’fand-Dorfman bialgebra,（A,[,]） be trivial and（A,o） be trivial. If A₁o A₁=0or [A₀, A₁]=0,（A,[,],o） is trivial.2. For dim A₀=1, there are2classes of nontrivial super Gel’fand-Dorfmanbialgebras.3. For dim A₀=2and dim A₁o A₁=1, there are67classes of nontrivial superGel’fand-Dorfman bialgebras.4. For dim A₀=2and dim A₁o A₁=2, there are3classes of nontrivial superGel’fand-Dorfman bialgebras.5. For dim A₀=3, there are211classes of nontrivial super Gel’fand-Dorfmanbialgebras.