On the ghost centre of Lie superalgebras
Annales de l'Institut Fourier, Tome 50 (2000) no. 6, pp. 1745-1764.

On étudie les invariantes de l’algèbre enveloppante d’une super algèbre de Lie par rapport à une action adjointe “tordue”.

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

@article{AIF_2000__50_6_1745_0,
     author = {Gorelik, Maria},
     title = {On the ghost centre of {Lie} superalgebras},
     journal = {Annales de l'Institut Fourier},
     pages = {1745--1764},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {50},
     number = {6},
     year = {2000},
     doi = {10.5802/aif.1806},
     mrnumber = {2002c:17017},
     zbl = {01544080},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1806/}
}
TY  - JOUR
AU  - Gorelik, Maria
TI  - On the ghost centre of Lie superalgebras
JO  - Annales de l'Institut Fourier
PY  - 2000
SP  - 1745
EP  - 1764
VL  - 50
IS  - 6
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1806/
DO  - 10.5802/aif.1806
LA  - en
ID  - AIF_2000__50_6_1745_0
ER  - 
%0 Journal Article
%A Gorelik, Maria
%T On the ghost centre of Lie superalgebras
%J Annales de l'Institut Fourier
%D 2000
%P 1745-1764
%V 50
%N 6
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.1806/
%R 10.5802/aif.1806
%G en
%F AIF_2000__50_6_1745_0
Gorelik, Maria. On the ghost centre of Lie superalgebras. Annales de l'Institut Fourier, Tome 50 (2000) no. 6, pp. 1745-1764. doi : 10.5802/aif.1806. http://www.numdam.org/articles/10.5802/aif.1806/

[ABF] D. Arnaudon, M. Bauer, L. Frappat, On Casimir's Ghost, Comm. Math. Phys., 187-2 (1997), 429-439. | MR | Zbl

[AL] M. Aubry and J.-M. Lemaire, Zero divisors in enveloping algebras of graded Lie algebras, J. Pure Appl. Algebra, 38 (1985), 159-166. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[Ch] S. Chelma, Propriétés de dualité dans les représentations coinduites de super-algèbres de Lie, Ann. Inst. Fourier, 44-4 (1994), 1067-1090. | Numdam | Zbl

[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. | MR | Zbl

[GL] M. Gorelik, E. Lanzmann, The minimal primitive spectrum of the enveloping algebra of the Lie superalgebra osp(1, 2l), preprint 1999. | Zbl

[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). | MR | Zbl

[J] A. Joseph, Sur l'annulateur d'un module de Verma, in Representation theories and algebraic geometry, ed. A. Broer, 1998.

[K1] V. G. Kac, Lie superalgebras, Adv. in Math., 26 (1977), 8-96. | MR | Zbl

[K2] V. G. Kac, Representations of classical Lie superalgebras, Lecture Notes in Math., 676 (1978), 597-626. | MR | Zbl

[LM] E. S. Letzter, I. M. Musson, Complete sets of representations of classical Lie superalgebras, Lett. Math. Phys., 31 (1994), 247-253. | MR | Zbl

[Mu1] I. M. Musson, On the center of the enveloping algebra of a classical simple Lie superalgebra, J. of Algebra, 193 (1997), 75-101. | MR | Zbl

[Mu2] I. M. Musson, On the Goldie quotient ring of the enveloping algebra of a classical simple Lie superalgebra, preprint 1999. | Zbl

[Sch] M. Scheunert, Invariant supersymmetric multilinear forms and Casimir elements of P-type Lie superalgebras, J. Math. Phys., 28-5 (1987), 1180-1191. | MR | Zbl

[S1] A. N. Sergeev, Invariant polynomial functions on Lie superalgebras, C. R. Acad. Bulgare Sci., 35-5 (1982), 573-576. | MR | Zbl

[S2] A. N. Sergeev, The invariant polynomials on simple Lie superalgebras, math. RT/9810111. | Zbl

Cité par Sources :