Pi-envelopes of Lie superalgebras
HTML articles powered by AMS MathViewer
- by Yuri Bahturin and Susan Montgomery
- Proc. Amer. Math. Soc. 127 (1999), 2829-2839
- DOI: https://doi.org/10.1090/S0002-9939-99-04825-X
- Published electronically: April 23, 1999
- PDF | Request permission
Abstract:
In this paper we find necessary and sufficient conditions on a finite-dimensional 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.References
- Yu. A. Bahturin, On the structure of the PI-envelope of a finite-dimensional Lie algebra, Soviet Math. (Iz. VUZ) 29 (1985) no. 11, 83-87.
- Yuri A. Bahturin, Alexander A. Mikhalev, Viktor M. Petrogradsky, and Mikhail V. Zaicev, Infinite-dimensional Lie superalgebras, De Gruyter Expositions in Mathematics, vol. 7, Walter de Gruyter & Co., Berlin, 1992. MR 1192546, DOI 10.1515/9783110851205
- Jeffrey Bergen and Miriam Cohen, Actions of commutative Hopf algebras, Bull. London Math. Soc. 18 (1986), no. 2, 159–164. MR 818820, DOI 10.1112/blms/18.2.159
- Yu. V. Billig, A homomorphic image of a special Lie algebra, Mat. Sb. (N.S.) 136(178) (1988), no. 3, 320–323, 430 (Russian); English transl., Math. USSR-Sb. 64 (1989), no. 2, 319–322. MR 959484, DOI 10.1070/SM1989v064n02ABEH003310
- Stefan Kempisty, Sur les fonctions à variation bornée au sens de Tonelli, Bull. Sém. Math. Univ. Wilno 2 (1939), 13–21 (French). MR 46
- Y. Bahturin, M.Zaicev, Identities of graded Lie algebras, J. Algebra 205 (1998), 1–12.
- M. Cohen and S. Montgomery, Group-graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), no. 1, 237–258. MR 728711, DOI 10.1090/S0002-9947-1984-0728711-4
- Miriam Cohen and Louis H. Rowen, Group graded rings, Comm. Algebra 11 (1983), no. 11, 1253–1270. MR 696990, DOI 10.1080/00927878308822904
- Michel Duflo, Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semi-simple, Ann. of Math. (2) 105 (1977), no. 1, 107–120. MR 430005, DOI 10.2307/1971027
- Daniel R. Farkas, Semisimple representations and affine rings, Proc. Amer. Math. Soc. 101 (1987), no. 2, 237–238. MR 902534, DOI 10.1090/S0002-9939-1987-0902534-3
- V. G. Kac, Lie superalgebras, Advances in Math. 26 (1977), no. 1, 8–96. MR 486011, DOI 10.1016/0001-8708(77)90017-2
- S. Montgomery, Constructing simple Lie superalgebras from associative graded algebras, J. Algebra 195 (1997), 558 - 579.
- H. Pop, A generalization of Scheunert’s theorem on cocycle twisting of Lie color algebras, preprint, q-alg 9703002.
- M. Scheunert, Generalized Lie algebras, J. Math. Phys. 20 (1979), no. 4, 712–720. MR 529734, DOI 10.1063/1.524113
- Manfred Scheunert, The theory of Lie superalgebras, Lecture Notes in Mathematics, vol. 716, Springer, Berlin, 1979. An introduction. MR 537441, DOI 10.1007/BFb0070929
Bibliographic Information
- Yuri Bahturin
- Affiliation: Department of Algebra, Moscow State University, 119899 Moscow, Russia
- MR Author ID: 202355
- Email: bahturin@mech.math.msu.su
- Susan Montgomery
- Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113
- Email: smontgom@math.usc.edu
- Received by editor(s): May 27, 1997
- Received by editor(s) in revised form: December 11, 1997
- Published electronically: April 23, 1999
- Additional Notes: The authors were supported by NSF grant DMS-9500649
- Communicated by: Lance W. Small
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2829-2839
- MSC (1991): Primary 17A70, 16W50
- DOI: https://doi.org/10.1090/S0002-9939-99-04825-X
- MathSciNet review: 1600092