×

zbMATH — the first resource for mathematics

Goldie rank in the enveloping algebra of a semisimple Lie algebra. III. (English) Zbl 0482.17002

MSC:
17B35 Universal enveloping (super)algebras
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16Dxx Modules, bimodules and ideals in associative algebras
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Barbasch, D; Vogan, D, Primitive ideals and orbital integrals in complex classical groups, (1981), Rutgers-M.I.T, preprint
[2] Bernstein, I.N; Gelfand, S.I, Tensor products of finite and infinite dimensional representations of semisimple Lie algebras, Composition math., 41, 245-285, (1980) · Zbl 0445.17006
[3] Borho, W, Primitive vollprime ideale in der einhüllenden von so(5, \(C\)), J. algebra, 43, 619-654, (1976) · Zbl 0346.17013
[4] Borho, W, Über schichten halbeinfacher Lie-algebren, (1981), preprint, Paris · Zbl 0484.17004
[5] Borho, W; Jantzen, J.C, Über primitive ideale in der einhüllenden einer halbeinfacher Lie-algebra, Invent. math., 39, 1-53, (1977) · Zbl 0327.17002
[6] Borho, W; Kraft, H, Über bahnen und deren deformationen bei linearen aktionen reduktiver gruppen, Comment. math. helv., 54, 61-104, (1979) · Zbl 0395.14013
[7] Cohn, P.M, Skew field constructions, () · Zbl 0355.16009
[8] Conze-Berline, N; Duflo, M, Sur LES représentations induites des groupes semisimples complexes, Compositio math., 34, 307-336, (1977) · Zbl 0389.22016
[9] Delorme, P, Extensions dans la categorie \(O\) de Bernstein-Gelfand-Gelfand, Applications, (1979), preprint, Paris
[10] Dixmier, J, Algèbres enveloppantes, () · Zbl 0422.17003
[11] Duflo, M, Représentations irréductibles des groupes semisimples complexes, (), 26-88
[12] Duflo, M, Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semisimple, Ann. of math., 105, 107-130, (1977) · Zbl 0346.17011
[13] Gabber, O; Joseph, A, On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula, Compositio math., 43, 107-131, (1981) · Zbl 0461.17004
[14] {\scO. Gabber and A. Joseph}, Towards the Kazhdan-Lusztig conjecture, Ann. Ec. Norm. Sup., in press. · Zbl 0476.17005
[15] Jacobson, N, Structure of rings, () · JFM 65.1131.01
[16] Jantzen, J.C, Moduln mit einem höchten gewicht, () · Zbl 0426.17001
[17] Joseph, A, The minimal orbit in a simple Lie algebra and its associated maximal ideal, Ann. école norm. sup., 9, 1-30, (1976) · Zbl 0346.17008
[18] Joseph, A, A characteristic variety for the primitive spectrum of a semisimple Lie algebra, (), 102-118, unpublished
[19] Joseph, A, On the annihilators of simple subquotients of the principal series, Ann. école norm. sup., 10, 419-440, (1977) · Zbl 0386.17004
[20] Joseph, A, Towards the jantzen conjecture, Compositio math., 40, 35-67, (1980) · Zbl 0424.17004
[21] Joseph, A, Gelfand-Kirillov dimension for the annihilators of simple quotients of Verma modules, J. London math. soc., 18, 50-60, (1978) · Zbl 0401.17007
[22] Joseph, A, Dixmier’s problem for Verma and principal series submodules, J. London math. soc., 20, 193-204, (1979) · Zbl 0421.17005
[23] Joseph, A, W-module structure in the primitive spectrum of the enveloping algebra of a semisimple Lie algebra, (), 116-135
[24] Joseph, A, Goldie rank in the enveloping algebra of a semisimple Lie algebra, I, J. algebra, 66, 269-283, (1980) · Zbl 0441.17004
[25] Joseph, A, Goldie rank in the enveloping algebra of a semisimple Lie algebra, II, J. algebra, 66, 284-306, (1980) · Zbl 0441.17004
[26] Joseph, A, Kostant’s problem, Goldie rank and the Gelfand-Kirillov conjecture, Invent. math., 56, 191-213, (1980) · Zbl 0446.17006
[27] Joseph, A, Kostant’s problem and Goldie rank, (), in press · Zbl 0468.17004
[28] Joseph, A; Small, L.W, An additivity principle for Goldie rank, Israel J. math., 31, 105-114, (1978) · Zbl 0395.17010
[29] Kazhdan, D.A; Lusztig, G, Representations of Coxeter groups and Hecke algebras, Invent. math., 53, 165-184, (1979) · Zbl 0499.20035
[30] Springer, T.A, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. math., 36, 173-207, (1976) · Zbl 0374.20054
[31] Springer, T.A, A construction of representations of Weyl groups, Invent. math., 44, 279-293, (1978) · Zbl 0376.17002
[32] Vogan, D.A, Ordering of the primitive spectrum of a semisimple Lie algebra, Math. ann., 248, 195-203, (1980) · Zbl 0414.17006
[33] Vogan, D.A, A generalized τ-invariant for the primitive spectrum of a semisimple Lie algebra, Math. ann., 242, 209-224, (1979) · Zbl 0387.17007
[34] Vogan, D.A, Irreducible characters of semisimple Lie groups I, Duke math. J., 46, 61-108, (1979) · Zbl 0398.22021
[35] {\scD. A. Vogan}, Irreducible characters of semisimple Lie groups II, The Kazhdan-Lusztig conjectures, Duke Math. J., in press. · Zbl 0421.22008
[36] {\scJ.-L. Brylinski and M. Kashiwara}, Démónstration de la conjecture de Kazhdan-Lusztig sur les modules de Verma, Compt. Rend., in press. · Zbl 0457.22012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.