In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i...In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.展开更多
The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm $G = \mathop \oplus \limits_{i \geqslant - 1} G_i $ must...The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm $G = \mathop \oplus \limits_{i \geqslant - 1} G_i $ must be isomorphic toW(m,n, 1) if the dimension ofG i satisfies a certain condition.展开更多
文摘In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
文摘The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm $G = \mathop \oplus \limits_{i \geqslant - 1} G_i $ must be isomorphic toW(m,n, 1) if the dimension ofG i satisfies a certain condition.
