N=2超代数的一类子代数的研究

A Study of One Lie Sub-superalgebra of the N = 2 Superconformal Algebras

主要研究了N=2超代数的一类子代数N的结构。首先,通过计算N的2-上同调群确定了它的泛中心扩张;其次,证明了N的所有导子都是内导子;最后,确定了N的自同构群的结构。

We mainly study the structures of the N = 2 sub-superalgebra. Firstly,the universal central extension of N is given by calculating the second cohomology group with trivial coefficients for N. Secondly, the derivation algebra of N is determined and it is proved that N has only inner derivation. Finally,the structures of the automorphism groups of N are characterized.