*-products in the method of orbits for nilpotent groups

DOI10.1016/0393-0440(85)90010-5zbMath0599.22012OpenAlexW2005398179MaRDI QIDQ1080536

J. C. Cortet, Didier Arnal

Publication date: 1985

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(85)90010-5

zbMATH Keywords

nilpotent Lie groupunitary irreducible representationsVon Neumann algebras

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Unitary representations of locally compact groups (22D10) Nilpotent and solvable Lie groups (22E25)

Related Items

Covariant deformations on polarized orbits of a Lie group, Paramétrisation du dual d'une algèbre de Lie nilpotente. (Parametrization of the dual of a nilpotent Lie algebra), Quantum groups and deformation quantization: Explicit approaches and implicit aspects, Homogeneous star products and closed integral formulas, Explicit star products on orbits of nilpotent Lie groups with square integrable representations, Symbolic calculus on nilpotent Lie groups and applications, Separation of coadjoint orbits of an exponential group by their convex envelops, \(*\)-representations of semisimple compact Lie groups, \(*\)- regular representation of compact Lie groups, The Paley-Wiener theorem for certain nilpotent Lie groupsJean, Deformations on coadjoint orbits, Differential cohomology of \(C^\infty ({\mathfrak G}^*)\), Group actions in deformation quantization, Q.U.P. and Paley-Wiener properties of unimodular, especially nilpotent, Lie groups, Représentations \({}^*\) des groupes exponentiels. \((^*\)- representations of exponential groups), Star representations of E(2), On the nilpotent \(*\)-Fourier transform, Symmetric spaces and star representations. II: Causal symmetric spaces

Cites Work

• An associative algebra of functions on the orbits of nilpotent Lie groups
• Quantum mechanics in phase space
• Deformation theory and quantization. I: Deformations of symplectic structures
• * products and representations of nilpotent groups
• The \(C^ *\)-algebras of a free Boson field
• UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
• Covariance and geometrical invariance in *quantization
• Analytic and Entire Vectors for Representations of Lie Groups
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