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Spectral synthesis for flat orbits in the dual space of weighted group algebras of nilpotent Lie groups

Authors: J. Ludwig, C. Molitor-Braun and D. Poguntke
Journal: Trans. Amer. Math. Soc. 365 (2013), 4433-4473
MSC (2010): Primary 22E30, 22E27, 43A20
Published electronically: December 5, 2012
MathSciNet review: 3055701
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Abstract: Let $ G=\mathrm {exp}(\mathfrak{g})$ be a connected, simply connected, nilpotent Lie group and let $ \omega $ be a continuous symmetric weight on $ G$ with polynomial growth. We determine the structure of all the two-sided closed ideals of the weighted group algebra $ L^1_{\omega }(G)$ which are attached to a flat co-adjoint orbit.

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Additional Information

J. Ludwig
Affiliation: Laboratoire LMAM, UMR 7122, Université de Lorraine, Ile de Saulcy, F-57045 Metz cedex 1, France

C. Molitor-Braun
Affiliation: Unité de Recherche en Mathématiques, Université du Luxembourg, 6, rue Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg

D. Poguntke
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

Keywords: Nilpotent Lie group, irreducible representation, co-adjoint orbit, flat orbit, minimal ideal, spectral synthesis, weighted group algebra
Received by editor(s): April 13, 2010
Received by editor(s) in revised form: February 1, 2012
Published electronically: December 5, 2012
Additional Notes: The second author was supported by the research grant 10NCHA of the University of Luxembourg
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.