On the ghost centre of Lie superalgebras
Gorelik, Maria
Annales de l'Institut Fourier, Tome 50 (2000), p. 1745-1764 / Harvested from Numdam
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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.

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     author = {Gorelik, Maria},
     title = {On the ghost centre of Lie superalgebras},
     journal = {Annales de l'Institut Fourier},
     volume = {50},
     year = {2000},
     pages = {1745-1764},
     doi = {10.5802/aif.1806},
     mrnumber = {2002c:17017},
     zbl = {01544080},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2000__50_6_1745_0}
}

Gorelik, Maria. On the ghost centre of Lie superalgebras. Annales de l'Institut Fourier, Tome 50 (2000) pp. 1745-1764. doi : 10.5802/aif.1806. http://gdmltest.u-ga.fr/item/AIF_2000__50_6_1745_0/

[ABF] D. Arnaudon, M. Bauer, L. Frappat, On Casimir's Ghost, Comm. Math. Phys., 187-2 (1997), 429-439. | MR 98h:17010 | Zbl 0888.17002

[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 87a:17022 | Zbl 0587.55006

[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 93c:17049 | Zbl 0811.16013

[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 54 #12988 | Zbl 0348.43007

[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 0815.17022

[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 53 #3045 | Zbl 0313.17005

[GL] M. Gorelik, E. Lanzmann, The minimal primitive spectrum of the enveloping algebra of the Lie superalgebra osp(1, 2l), preprint 1999. | Zbl 01539370

[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 95c:17013 | Zbl 0811.17002

[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 58 #5803 | Zbl 0366.17012

[K2] V. G. Kac, Representations of classical Lie superalgebras, Lecture Notes in Math., 676 (1978), 597-626. | MR 80f:17006 | Zbl 0388.17002

[LM] E. S. Letzter, I. M. Musson, Complete sets of representations of classical Lie superalgebras, Lett. Math. Phys., 31 (1994), 247-253. | MR 95g:17008 | Zbl 0804.17001

[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 98k:17012 | Zbl 0885.17007

[Mu2] I. M. Musson, On the Goldie quotient ring of the enveloping algebra of a classical simple Lie superalgebra, preprint 1999. | Zbl 01563179

[Sch] M. Scheunert, Invariant supersymmetric multilinear forms and Casimir elements of P-type Lie superalgebras, J. Math. Phys., 28-5 (1987), 1180-1191. | MR 89b:17008 | Zbl 0622.17002

[S1] A. N. Sergeev, Invariant polynomial functions on Lie superalgebras, C. R. Acad. Bulgare Sci., 35-5 (1982), 573-576. | MR 84h:17015 | Zbl 0501.17003

[S2] A. N. Sergeev, The invariant polynomials on simple Lie superalgebras, math. RT/9810111. | Zbl 01460683