On the ghost centre of Lie superalgebras

Maria Gorelik

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 6, page 1745-1764
  • ISSN: 0373-0956

Abstract

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We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.

How to cite

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Gorelik, Maria. "On the ghost centre of Lie superalgebras." Annales de l'institut Fourier 50.6 (2000): 1745-1764. <http://eudml.org/doc/75470>.

@article{Gorelik2000,
abstract = {We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.},
author = {Gorelik, Maria},
journal = {Annales de l'institut Fourier},
keywords = {Lie superalgebras; universal enveloping algebra; adjoint action},
language = {eng},
number = {6},
pages = {1745-1764},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the ghost centre of Lie superalgebras},
url = {http://eudml.org/doc/75470},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Gorelik, Maria
TI - On the ghost centre of Lie superalgebras
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 6
SP - 1745
EP - 1764
AB - We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.
LA - eng
KW - Lie superalgebras; universal enveloping algebra; adjoint action
UR - http://eudml.org/doc/75470
ER -

References

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  2. [AL] M. AUBRY and J.-M. LEMAIRE, Zero divisors in enveloping algebras of graded Lie algebras, J. Pure Appl. Algebra, 38 (1985), 159-166. Zbl0587.55006MR87a:17022
  3. [BF] A. D. BELL and R. FARNSTEINER, On the theory of Frobenius extensions and its application to Lie superalgebras, Trans AMS, 335-1 (1993), p. 407-424. Zbl0811.16013MR93c:17049
  4. [BZ] J. BERNSTEIN, A. ZELEVINSKY, Representations of the group GL(n, F), where F is a local non-Archimedean field, Uspekhi Mat. Nauk (Russian), 31-3 (1976), 5-70. Zbl0348.43007MR54 #12988
  5. [Ch] S. CHELMA, Propriétés de dualité dans les représentations coinduites de super-algèbres de Lie, Ann. Inst. Fourier, 44-4 (1994), 1067-1090. Zbl0815.17022
  6. [D] M. DUFLO, Construction of primitive ideals in an enveloping algebra, in: I. M. Gelfand, ed.. Publ. of 1971 Summer School in Math., Janos Bolyai Math. Soc., Budapest, 77-93. Zbl0313.17005MR53 #3045
  7. [GL] M. GORELIK, E. LANZMANN, The minimal primitive spectrum of the enveloping algebra of the Lie superalgebra osp(1, 2l), preprint 1999. Zbl1045.17004
  8. [Ja] H. P. JAKOBSEN, The full set of unitarizable highest weight modules of basic classical Lie superalgebras, Memoirs of the Amer. Math. Soc., 532 (1994). Zbl0811.17002MR95c:17013
  9. [J] A. JOSEPH, Sur l'annulateur d'un module de Verma, in Representation theories and algebraic geometry, ed. A. Broer, 1998. 
  10. [K1] V. G. KAC, Lie superalgebras, Adv. in Math., 26 (1977), 8-96. Zbl0366.17012MR58 #5803
  11. [K2] V. G. KAC, Representations of classical Lie superalgebras, Lecture Notes in Math., 676 (1978), 597-626. Zbl0388.17002MR80f:17006
  12. [LM] E. S. LETZTER, I. M. MUSSON, Complete sets of representations of classical Lie superalgebras, Lett. Math. Phys., 31 (1994), 247-253. Zbl0804.17001MR95g:17008
  13. [Mu1] I. M. MUSSON, On the center of the enveloping algebra of a classical simple Lie superalgebra, J. of Algebra, 193 (1997), 75-101. Zbl0885.17007MR98k:17012
  14. [Mu2] I. M. MUSSON, On the Goldie quotient ring of the enveloping algebra of a classical simple Lie superalgebra, preprint 1999. Zbl1018.16014
  15. [Sch] M. SCHEUNERT, Invariant supersymmetric multilinear forms and Casimir elements of P-type Lie superalgebras, J. Math. Phys., 28-5 (1987), 1180-1191. Zbl0622.17002MR89b:17008
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