Journal of Lie Theory 25 (2015), No. 3, 613--655
Copyright Heldermann Verlag 2015
C*-Algebras with Norm Controlled Dual Limits and Nilpotent Lie Groups
Jean Ludwig
Institut Elie Cartan, Université de Lorraine, 57045 Metz, France
jean.ludwig@univ-lorraine.fr
Hedi Regeiba
Institut Elie Cartan, Université de Lorraine, 57045 Metz, France
hedi.regeiba@univ-lorraine.fr
Motivated by the description of the C*-algebras of 5-dimensional nilpotent Lie groups as algebras of operator fields defined over their spectra, we introduce the family of C*-algebras with norm controlled dual limits and we show by explicit computations that the C*-algebras of every 5-dimensional nilpotent Lie group belong to this class.
Keywords: 5-dimensional nilpotent Lie groups, C*-algebras of Lie groups, algebras of operator fields, Fourier transform.
MSC: 22D25, 22D10, 43A10, 43A20, 46L45
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