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 -
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] On Casimir's Ghost, Comm. Math. Phys., 187-2 (1997), 429-439. | MR | Zbl
, , ,[AL] Zero divisors in enveloping algebras of graded Lie algebras, J. Pure Appl. Algebra, 38 (1985), 159-166. | MR | Zbl
and ,[BF] On the theory of Frobenius extensions and its application to Lie superalgebras, Trans AMS, 335-1 (1993), p. 407-424. | MR | Zbl
and ,[BZ] 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] Propriétés de dualité dans les représentations coinduites de super-algèbres de Lie, Ann. Inst. Fourier, 44-4 (1994), 1067-1090. | Numdam | Zbl
,[D] 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] The minimal primitive spectrum of the enveloping algebra of the Lie superalgebra osp(1, 2l), preprint 1999. | Zbl
, ,[Ja] The full set of unitarizable highest weight modules of basic classical Lie superalgebras, Memoirs of the Amer. Math. Soc., 532 (1994). | MR | Zbl
,[J] Sur l'annulateur d'un module de Verma, in Representation theories and algebraic geometry, ed. A. Broer, 1998.
,[K1] Lie superalgebras, Adv. in Math., 26 (1977), 8-96. | MR | Zbl
,[K2] Representations of classical Lie superalgebras, Lecture Notes in Math., 676 (1978), 597-626. | MR | Zbl
,[LM] Complete sets of representations of classical Lie superalgebras, Lett. Math. Phys., 31 (1994), 247-253. | MR | Zbl
, ,[Mu1] On the center of the enveloping algebra of a classical simple Lie superalgebra, J. of Algebra, 193 (1997), 75-101. | MR | Zbl
,[Mu2] On the Goldie quotient ring of the enveloping algebra of a classical simple Lie superalgebra, preprint 1999. | Zbl
,[Sch] Invariant supersymmetric multilinear forms and Casimir elements of P-type Lie superalgebras, J. Math. Phys., 28-5 (1987), 1180-1191. | MR | Zbl
,[S1] Invariant polynomial functions on Lie superalgebras, C. R. Acad. Bulgare Sci., 35-5 (1982), 573-576. | MR | Zbl
,[S2] The invariant polynomials on simple Lie superalgebras, math. RT/9810111. | Zbl
,Cité par Sources :