Virasoro李代数的子代数间的同构及生成元

证明了无中心Virasoro李代数的有限维子代数同构的充分必要条件,证明了两个元素di,dj作为生成元的充分必要条件,找出了几组互相同构的无限维真子代数,研究了他们的极大性,单性以及其它性质.

Isomorphism and Generating Sets of Subalgebras of the VirasoroAlgebra

In this paper, the isomorphisms between subalgebras of the Virasoro algebra are discussed. The generating sets, simplicities and maximal properties of the subalgebras are also studied. In particular, it is obtained that $d_i$ and $d_j$ are the minimal generators if and only if $i$ and $j$ are coprime integers with different sign and with absolute value bigger than 1. Also $g_1\cong g_2$ if and only if ${\rm dim\,}g_1={\rm dim\,}g_2$.