The Classification Of A Class Of Homogeneous Borel Subalgebras Of H(2)

The classification of homogeneous Borel subalgebras in Lie algebras of positive characteristic has always been concerned by academia.For Lie algebras of Cartan type,the conjugate classification probelme of homogeneous Borel subalgebras of lie algebras of W(n)type has been solved,but for Lie algebras of type H(2r),S(n),K(n),there is no significant progress in this problem.The conjugate classification of homogeneous Borel subalgebras in the case of r = 1 for Lie algebras of H(2r)type on the field of positive characteristic has been obtained partly in this paper.We use the classification of homogeneous Lie subalgebras in polynomial algebra to solve the conjugate classi-fication problem of homogeneous Borel subalgebras in Lie algebras of Cartan type for the first time.In this paper,we create the concept of index δ,index of σ,index of ε,ho-mogeneous Lie subalgebras for the first time,and these are also innovative ideas in this paper to study the solvability of Lie algebras and the classification of Borel subalgebras.