A surjectivity theorem for rigid highest weight modules

DOI10.1007/BF01393748zbMath0657.17004OpenAlexW2058439436MaRDI QIDQ1110640

Anthony Joseph

Publication date: 1988

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143583

zbMATH Keywords

universal enveloping algebraCartan subalgebrahighest weight modulecomplex semisimple Lie algebracompletely prime idealsurjectivity theoremcompletely prime primitive idealsGoldie skew fieldinjection mapprimitive quotient

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47) Division rings and semisimple Artin rings (16Kxx)

Related Items (12)

Annihilators and associated varieties of unitary highest weight modules ⋮ Lie superalgebras, Clifford algebras, induced modules and nilpotent orbits ⋮ On the characteristic polynomials of orbital varieties ⋮ Derived subalgebras of centralisers and finite -algebras ⋮ Higher symmetries of powers of the Laplacian and rings of differential operators ⋮ Orbital varieties of the minimal orbit ⋮ On the Kostant-Parthasarathy-Ranga Rao-Varadarajan determinants. I: Injectivity and multiplicities ⋮ Sheets and topology of primitive spectra for semisimple Lie algebras ⋮ A triangularity result for associated varieties of highest weight modules ⋮ Modules for relative Yangians (family algebras) and Kazhdan-Lusztig polynomials ⋮ Mœglin’s theorem and Goldie rank polynomials in Cartan type A ⋮ On the Brylinski-Kostant filtration

Cites Work

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• Goldie rank in the enveloping algebra of a semisimple Lie algebra. I, II
• Kostant's problem, Goldie rank and the Gelfand-Kirillov conjecture
• A preparation theorem for the prime spectrum of a semisimple Lie algebra
• Differential operators on homogeneous spaces. I: Irreducibility of the associated variety for annihilators of induced modules
• The structure of the Lie field connected with a split semisimple Lie algebra
• Modules of t-Finite Vectors Over Semi-Simple Lie Algebras
• A Generalization of the Gelfand-Kirillov Conjecture
• Gelfand-Kirillov Dimension for the Annihilators of Simple Quotients of Verma Modules

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