A generalization of Quillen's lemma and its application to the Weyl algebras

DOI10.1007/BF02759808zbMath0366.17006WikidataQ124792134 ScholiaQ124792134MaRDI QIDQ1241793

Anthony Joseph

Publication date: 1977

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Weyl algebrasKrull dimensionenveloping algebra of finite dimensional Lie algebraQuillen's lemma

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Localization and associative Noetherian rings (16P50) Division rings and semisimple Artin rings (16Kxx)

Related Items (25)

The noncommutative schemes of generalized Weyl algebras ⋮ Central localization and Gelfand-Kirillov dimension ⋮ Centralisateurs dans les lorps de weyl ⋮ Krull dimensions of the enveloping algebra of sl(2,C) ⋮ Fixed rings of quantum generalized Weyl algebras ⋮ Generic flatness for strongly Noetherian algebras ⋮ Filter dimension of algebras and modules, a simplicity criterion of generalized weyl algebras ⋮ The kernel of an homomorphism of Harish-Chandra ⋮ Simple holonomic modules over the second Weyl algebra \(A_2\) ⋮ Noncommutative deformations of Kleinian singularities ⋮ Krull dimension of factor rings of the enveloping algebra of a semi-simple Lie algebra ⋮ Endomorphism rings of modules and lattices of submodules ⋮ Filter Dimension ⋮ Sur les quotients premiers de l'algèbre enveloppante d'une algèbre de Lie résoluble, II ⋮ Braided doubles and rational Cherednik algebras. ⋮ Bimodules sur une algèbre de Lie résoluble. (Bimodules over a solvable Lie algebra) ⋮ Krull and global dimensions of Weyl algebras over division rings ⋮ Non-holonomic modules over Weyl algebras and enveloping algebras ⋮ Fixed rings of generalized Weyl algebras ⋮ Reflexive hull discriminants and applications ⋮ Gaudin models and multipoint conformal blocks. II: Comb channel vertices in 3D and 4D ⋮ The Differential Operator Ring of an Affine Curve ⋮ Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable ⋮ Primitivity in skew Laurent polynomial rings and related rings ⋮ Finiteness properties of subalgebras of the weyl algebra

Cites Work

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• Oresche Teilmengen in Einhüllenden Algebren. (Ore subsets in enveloping algebras)
• Über die Gelfand-Kirillov-Dimension. (On the Gelfand-Kirillov-dimension)
• A preparation theorem for the prime spectrum of a semisimple Lie algebra
• The analytic continuation of generalized functions with respect to a parameter
• Derivations of Lie brackets and canonical quantisation
• Commutativity of certain centralizers in the rings R\(_{n,k}\)
• The Weyl Algebra-Semisimple and Nilpotent Elements
• A wild automorphism ofUsl(2)
• Sur les algèbres de Weyl
• On the Endomorphism Ring of a Simple Module Over an Enveloping Algebra

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