一类李代数的滤过项的不变性

The Invariance of Natural Filtration for some Lie Algebras

研究了特征p>3的域F上有限维广义Witt型李超代数和S型李超代数的偶部滤过的结构.通过讨论ad-幂零元的方法确定了标准滤过各项在自同构群下的不变性,从而得出W和S型李超代数偶部的标准滤过在自同构群下的不变性.

Let F be a field of characteristic p3.g is a Lie algebra which is the even part of generalized Witt algebra or Special Lie algebra over.It is proved that the natural filtrations of the even part of generalized Witt algebra or Special Lie algebra over is invariant under their automorphism groups by means of investigating the ad-nilpotent elements.