摘要
Certain important results concerning p-envelopes of modular Lie algebras are generalized to the super-case. In particular, any p-envelope of the Lie algebra of a Lie superalgebra can be naturally extended to a restricted envelope of the Lie superalgebra. As an application, a theorem on the representations of Lie superalgebras is given, which is a super-version of Iwasawa＇s theorem in Lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular Lie superalgebras of Cartan type.
Certain important results concerning p-envelopes of modular Lie algebras are generalized to the super-case. In particular, any p-envelope of the Lie algebra of a Lie superalgebra can be naturally extended to a restricted envelope of the Lie superalgebra. As an application, a theorem on the representations of Lie superalgebras is given, which is a super-version of Iwasawa＇s theorem in Lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular Lie superalgebras of Cartan type.
