Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Pi-envelopes of Lie superalgebras


Authors: Yuri Bahturin and Susan Montgomery
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
Published electronically: April 23, 1999
MathSciNet review: 1600092
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [Ba 85] 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.
  • [BMPZ ] Yu. A. Bahturin, A. Mikhalev, V. Petrogradskii, M. Zaicev, Infinite Dimensional Lie Superalgebras, Expos. Math. vol 7, Walter de Gruyter, Berlin, 1992. MR 94b:17001
  • [BeC] J. Bergen and M. Cohen, Actions of commutative Hopf algebras, Bull. LMS 18 (1986), 159-164. MR 87e:16052
  • [Bi] Yuly Billig, On the homomorphic image of a special Lie algebra, Mat. Sc 136 (178)(1988), 320-323; English transl. in Math. USSR Sb. 64 (1989) MR 89k:17015
  • [Bl] R. J. Blattner, Induced and produced representations of Lie algebras, Transactions AMS 144 (1969), 457-474. MR 46i:7338a
  • [BZ] Y. Bahturin, M.Zaicev, Identities of graded Lie algebras, J. Algebra 205 (1998), 1-12. CMP 98:15
  • [CM] M. Cohen and S. Montgomery, Group-graded rings, smash products, and group actions, Trans. AMS 282 (1984), 237-258. MR 85i:16002
  • [CR] M. Cohen and L. Rowen, Group graded rings, Comm. Algebra 11 (1983), 1253 -1270. MR 85b:16002
  • [Du] M. Duflo, Sur la classification des ideaux primitifs dans l'algebre enveloppante d'une algebre de Lie semi-simple, Ann. Math. 105 (1977), 107-120. MR 55:3013
  • [Fa] D. Farkas, Semisimple representations and affine rings, Proc. AMS 101 (1987), 237 - 238. MR 88h:16027
  • [Kac] V. Kac, Lie superalgebras, Advances in Math. 26 (1977), 8-96. MR 58:5803
  • [Mo] S. Montgomery, Constructing simple Lie superalgebras from associative graded algebras, J. Algebra 195 (1997), 558 - 579. CMP 98:01
  • [Po] H. Pop, A generalization of Scheunert's theorem on cocycle twisting of Lie color algebras, preprint, q-alg 9703002.
  • [S79a] M. Scheunert, Generalized Lie algebras, J. Math Physics 20 (1979), 712-720. MR 80f:17007
  • [S79b] M. Scheunert, The Theory of Lie Superalgebras, Lecture Notes in Math., vol. 716, Springer-Verlag, Berlin, 1979. MR 80i:17005

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 17A70, 16W50

Retrieve articles in all journals with MSC (1991): 17A70, 16W50


Additional Information

Yuri Bahturin
Affiliation: Department of Algebra, Moscow State University, 119899 Moscow, Russia
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

DOI: https://doi.org/10.1090/S0002-9939-99-04825-X
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
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society