设W是素特征域上无限维或有限维广义Witt李超代数.本文利用W的自然滤过不变性和W的底代数的不变维数性质,证明了W的自同构群AutW同构于W的底代数的容许自同构群,还证明了在此群同构之下,AutW的标准正规列恰好对应W的底代数的容许自同构群的标准正规列,并给出AutW若干较为细致的性质.

Let W be the infinite-dimensional or finite-dimensional generalized Witt Lie superalgebra over a field of prime characteristic and Aut W the automorphism group. Employing the invariance of the natural filtration of W and the invariant dimension property of the base algebra of W, we prove that Aut W is isomorphic to the admissible automorphism group of the base algebra of W. Then it is proved that the group isomorphism sends the standard normal series of Aut W to the one of the admissible automorphism groups, and further properties of Aut W are given.