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Berechnung der Gelfand-Kirillov-Dimension bei induzierten Darstellungen. (German) Zbl 0346.17012

MSC:
17B35 Universal enveloping (super)algebras
16E10 Homological dimension in associative algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16Kxx Division rings and semisimple Artin rings
16Dxx Modules, bimodules and ideals in associative algebras
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References:
[1] Borel, A.: Linear algebraic groups. New York: Benjamin 1969 · Zbl 0206.49801
[2] Borho, W., Gabriel, P., Rentschler, R.: Primideale in Einhüllenden auflösbarer Lie-Algebren. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0293.17005
[3] Borho, W., Kraft, H.: Über die Gelfand-Kirillov-Dimension. Math. Ann.220, 1-24 (1976) · Zbl 0313.17004 · doi:10.1007/BF01354525
[4] Bourbaki, N.: Groupes et algèbres de Lie. Chap. IV?VI. Paris: Hermann 1968 · Zbl 0186.33001
[5] Conze, N.: Algèbres d’opérateurs différentiels et quotients des algèbres enveloppantes. Bull. Soc. Math. France102, 379-415 (1974) · Zbl 0298.17012
[6] Conce, N., Dixmier, J.: Idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semi-simple. Bull. Sci. Math.96, 339-351 (1972) · Zbl 0246.17009
[7] Dixmier, J.: Algèbres enveloppantes. Paris: Gauthier-Villars 1974 · Zbl 0308.17007
[8] Dixmier, J.: Idèaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semi-simple complexe. C.R. Acad. Sci.272, 1628-1630 (1971) · Zbl 0215.09504
[9] Jantzen, J. C.: Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren. Math. Ann. (erscheint demnächst) · Zbl 0372.17003
[10] Joseph, A.: The minimal orbit in a simple Lie-algebra and its associated maximal ideal. Ann. scient. Éc. Norm. Sup.9, 1-30 (1976) · Zbl 0346.17008
[11] Joseph, A.: Primitive ideals in the enveloping algebras ofsl 3 andsp 4. Preprint. Paris 1976
[12] Richardson, R. W.: Conjugacy classes in parabolic subgroups of semi-simple algebraic groups. Bull. London M.S.6, 21-24 (1974) · Zbl 0287.20036 · doi:10.1112/blms/6.1.21
[13] Borho, W., Jantzen, J. C.: Primitive Ideale in der Einhüllenden einer halbeinfachen Lie-Algebra. Inventiones math. (erscheint demnächst) · Zbl 0327.17002
[14] Grothendieck, A.: Revêtements étales et groupe fondamental (SGA 1). Berlin, Heidelberg, New York: Springer 1971 · Zbl 0234.14002
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