素特征域上的有限维李超代数∑

Finite-dimensional Lie superalgebras ∑ over a prime field

对于有限维模李超代数 (即特征 p >0的域上的李超代数 ) ,目前已有的结果尚少 .文献[4 ]构造了Cartan型模李超代数 .本文应用文献 [5 ]的方法 ,构造了有限维模李超代数 ,讨论了它的中心。

There are plentiful results about the finite-dimensional Lie superalgebras over a field of characteistic zero and their representations.But up to now there are only a few results about the finite-dimensional modular Lie superalgebras(i.e.the Lie superalgebras over a field of characteistic p>0).In refrence the modular Lie superalgebras of Cartan type are constructed.In this paper the finite-dimensional modular Lie superalgebras  is constructed by using the technique intruduced in ,and its centre,commutator subalgebra and simplicity are discussed.