99 Citations
Towards the Jantzen conjecture
- Mathematics
- 1980
Let g be a complex semisimple Lie algebra, U(g) its enveloping algebra, Prim U(g) the set of primitive ideals of U(g) and b a Cartan subalgebra for g. For g simple of type An-l (Cartan notation),…
On the Maximal Primitive Ideal Corresponding to the Model Nilpotent Orbit
- Mathematics
- 2012
Let g = k ⊕ s be a Cartan decomposition of a simple complex Lie algebra corresponding to the Chevalley involution. It is well known that among the set of primitive ideals with the infinitesimal…
Infinite Kostant cascades and centrally generated primitive ideals of U(n) in types A∞, C∞
- Mathematics
- 2016
On Dixmier–Duflo isomorphism in positive characteristic – The classical nilpotent case
- Mathematics
- 2013
1 9 Fe b 20 03 On Commutative Polarizations
- Mathematics
- 2003
Let L be a finite-dimensional Lie algebra over a field k of characteristic zero and let U(L) be its enveloping algebra with quotient division ring D(L). Let P be a commutative Lie subalgebra of L. In…
References
SHOWING 1-10 OF 32 REFERENCES
The minimal orbit in a simple Lie algebra and its associated maximal ideal
- Mathematics
- 1976
— Let 9 be a simple Lie algebra over C. If 9 is different from sl(n + 1) : n = 1, 2, ..., then g* admits a single non-trivial G-orbit (Po of minimal dimension. This orbit consists of nilpotent…
Gel'fand-Kirillov dimension for algebras associated with the Weyl algebra
- Mathematics
- 1972
Let K be a commutative field of characteristic zero. The Weyl algebra of degree n over K is defined as the associative algebra An (K) whose generators satisfy the canonical commutation relations for…
Sur la classification des ideaux primitifs dans l'algebre enveloppante d'une algebre de Lie semi-simple
- Mathematics
- 1977
Summary Let g be a semi-simple complex Lie algebra. We denote by U(g) its enveloping algebra. A (two-sided) ideal I of U(g) is called primitive if it is the kernel of an irreducible representation of…
Proof of the Gelfand-Kirillov conjecture for solvable Lie algebras
- Mathematics
- 1974
Let g be a solvable algebraic Lie algebra over the complex numbers C. It is shown that the quotient field of the enveloping algebra of g is isomorphic to one of the standard fields Dn A, being…
Lie Group Representations on Polynomial Rings
- Mathematics
- 1963
Let G be a group of linear transformations on a finite dimensional real or complex vector space X. Assume X is completely reducible as a G-module. Let S be the ring of all complex-valued polynomials…
Sur les représentations unitaires des groupes de Lie nilpotents. II
- Mathematics
- 1957
Soient T un groupe localement compact, T l'ensemble des classes de représentations unitaires irréductibles de T. Dans (4), Godement a défini une topologie sur T que nous appellerons "topologie…
La structure de Poisson sur l'algèbre symétrique d'une algèbre de Lie nilpotente
- Mathematics
- 1972
RÉSUMÉ. — Cet article traite du problème suivant : Soient 9 une algèbre de Lie niipotente, et G le groupe de Lie simplement connexe d'algèbre de Lie 9; les orbites de G dans 9* sont munies…
Sur les représentations induites des groupes semi-simples complexes
- Mathematics
- 1977
© Foundation Compositio Mathematica, 1977, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions…
Groupes et algèbres de Lie
- Philosophy
- 1971
Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements. Ce premier volume du Livre sur…