论文信息 - Pi-envelopes of Lie superalgebras

Pi-envelopes of Lie superalgebras

In this paper we find necessary and sufficient conditions on a finitedimensional Lie superalgebra under which any associative PI-envelope of L is finite-dimensional. We also extend M. Scheunert’s result which enables one to pass from color Lie superalgebras to the ordinary ones, to the case of gradings by an arbitrary abelian group.

Y. Bahturin | S. Montgomery

[1] Y. Bahturin,et al. Identities of Graded Algebras , 1998 .

[2] S. Montgomery. Constructing Simple Lie Superalgebras from Associative Graded Algebras , 1997 .

[3] Uwe Franz,et al. Generalized Lie Algebras , 1993 .

[4] Y. Bahturin. Infinite Dimensional Lie Superalgebras , 1992 .

[5] Y. Billig. On a Homomorphic Image of a Special Lie Algebra , 1989 .

[6] S. Montgomery,et al. Addendum to: “Group-graded rings, smash products, and group actions” [Trans. Amer. Math. Soc. 282 (1984), no. 1, 237–258; MR0728711 (85i:16002)] , 1987 .

[7] D. Farkas. Semisimple representations and affine rings , 1987 .

[8] Jeffrey Bergen,et al. Actions of Commutative Hopf Algebras , 1986 .

[9] S. Montgomery,et al. Group-graded rings, smash products, and group actions , 1984 .

[10] L. Rowen,et al. Group graded rings , 1983 .

[11] M. Scheunert,et al. The Theory of Lie Superalgebras: An Introduction , 1979 .

[12] M. Scheunert,et al. The Theory of Lie Superalgebras , 1979 .

[13] M. Duflo. Sur la classification des ideaux primitifs dans l'algebre enveloppante d'une algebre de Lie semi-simple , 1977 .

[14] R. Blattner. Induced and produced representations of Lie algebras , 1969 .