Annihilation Theorem and Separation Theorem for basic classical Lie superalgebras
Journal of the American Mathematical Society, Tome 15 (2002) no. 1, pp. 113-165

Voir la notice de l'article provenant de la source American Mathematical Society

In this article we prove that for a basic classical Lie superalgebra the annihilator of a strongly typical Verma module is a centrally generated ideal. For a basic classical Lie superalgebra of type I we prove that the localization of the enveloping algebra by a certain central element is free over its centre.
DOI : 10.1090/S0894-0347-01-00382-4

Gorelik, Maria  1

1 Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Gorelik, Maria. Annihilation Theorem and Separation Theorem for basic classical Lie superalgebras. Journal of the American Mathematical Society, Tome 15 (2002) no. 1, pp. 113-165. doi: 10.1090/S0894-0347-01-00382-4
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[1] Aubry, Marc, Lemaire, Jean-Michel Zero divisors in enveloping algebras of graded Lie algebras J. Pure Appl. Algebra 1985 159 166

[2] Bell, Allen D., Farnsteiner, Rolf On the theory of Frobenius extensions and its application to Lie superalgebras Trans. Amer. Math. Soc. 1993 407 424

[3] Bernstein, Joseph, Lunts, Valery A simple proof of Kostant’s theorem that 𝑈(𝔤) is free over its center Amer. J. Math. 1996 979 987

[4] Bershadsky, Michael, Zhukov, Slava, Vaintrob, Arkady 𝑃𝑆𝐿(𝑛|𝑛) sigma model as a conformal field theory Nuclear Phys. B 1999 205 234

[5] Duflo, Michel Construction of primitive ideals in an enveloping algebra 1975 77 93

[6] Gorelik, Maria, Lanzmann, Emmanuel The annihilation theorem for the completely reducible Lie superalgebras Invent. Math. 1999 651 680

[7] Gorelik, Maria, Lanzmann, Emmanuel The minimal primitive spectrum of the enveloping algebra of the Lie superalgebra 𝑜𝑠𝑝(1,2𝑙) Adv. Math. 2000 333 366

[8] Jantzen, Jens Carsten Einhüllende Algebren halbeinfacher Lie-Algebren 1983

[9] Joseph, A. Kostant’s problem, Goldie rank and the Gel′fand-Kirillov conjecture Invent. Math. 1980 191 213

[10] Joseph, Anthony Quantum groups and their primitive ideals 1995

[11] Joseph, Anthony Sur l’annulateur d’un module de Verma 1998 237 300

[12] Joseph, Anthony, Letzter, Gail Verma module annihilators for quantized enveloping algebras Ann. Sci. École Norm. Sup. (4) 1995 493 526

[13] Kac, V. G. Lie superalgebras Advances in Math. 1977 8 96

[14] Kac, V. G. Characters of typical representations of classical Lie superalgebras Comm. Algebra 1977 889 897

[15] Kac, V. Representations of classical Lie superalgebras 1978 597 626

[16] Kostant, Bertram Lie group representations on polynomial rings Amer. J. Math. 1963 327 404

[17] Letzter, Edward S., Musson, Ian M. Complete sets of representations of classical Lie superalgebras Lett. Math. Phys. 1994 247 253

[18] Mac Lane, Saunders Homology 1963

[19] Musson, Ian M. On the center of the enveloping algebra of a classical simple Lie superalgebra J. Algebra 1997 75 101

[20] Musson, Ian M. A classification of primitive ideals in the enveloping algebra of a classical simple Lie superalgebra Adv. Math. 1992 252 268

[21] Parthasarathy, K. R., Ranga Rao, R., Varadarajan, V. S. Representations of complex semi-simple Lie groups and Lie algebras Ann. of Math. (2) 1967 383 429

[22] Penkov, Ivan, Serganova, Vera Representations of classical Lie superalgebras of type 𝐼 Indag. Math. (N.S.) 1992 419 466

[23] Penkov, Ivan, Serganova, Vera Generic irreducible representations of finite-dimensional Lie superalgebras Internat. J. Math. 1994 389 419

[24] Scheunert, Manfred The theory of Lie superalgebras 1979

[25] Sergeev, A. N. Invariant polynomial functions on Lie superalgebras C. R. Acad. Bulgare Sci. 1982 573 576

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