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Primitive ideals with bounded approximate units in L1-algebras of exponential lie groups

Part of: Lie groups Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Mohammed El Bachir Bekka
Mohammed El Bachir Bekka
Affiliation:
Fachbereich Mathematik/Informatik, der Universität-Gesamthochschule Paderborn, Warburgerstr. 100, D-4790 Paderborn, Federal Republic of Germany
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Abstract

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Let G be an exponential Lie group. We study primitive ideals (i.e. kernels of irreducible *-representations of L1(G)), with bounded approximate units (b.a.u.). We prove a result relating the existence of b.a.u. in certain primitive ideals with the geometry of the corresponding Kirillov orbits. This yields for a solvable group of class 2, a characterization of the primitive ideals with b.a.u.

MSC classification

Secondary: 43A20: $L^1$-algebras on groups, semigroups, etc. 22E30: Analysis on real and complex Lie groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 3 , December 1986 , pp. 411 - 420
Copyright
Copyright © Australian Mathematical Society 1986

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