Completely prime ideals of the enveloping algebra of \(\mathfrak{gl}_ n({\mathbb{C}})\)).

DOI10.1016/0021-8693(87)90001-9zbMath0637.17005OpenAlexW1964158121MaRDI QIDQ1098921

Colette Moeglin

Publication date: 1987

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90001-9

zbMATH Keywords

universal enveloping algebraparabolic subalgebrainduced representationprimitive idealcompletely prime ideal

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Semisimple Lie groups and their representations (22E46) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Simple, semisimple, reductive (super)algebras (17B20) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

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Cites Work

• Oresche Teilmengen in Einhüllenden Algebren. (Ore subsets in enveloping algebras)
• Über die Gelfand-Kirillov-Dimension. (On the Gelfand-Kirillov-dimension)
• Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie- Algebra
• Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple
• Definition einer Dixmier-Abbildung für \(\mathfrak{sl}(n,\mathbb C)\)
• Primitive ideals in enveloping algebras
• Réduction de produits semi-directs et conjecture de Gel'fand et Kirillov
• Sur la classification des idéaux primitifs des algèbres enveloppantes
• Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes
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