Reference : The C*-algebras of certain Lie groups
Dissertations and theses : Doctoral thesis
Physical, chemical, mathematical & earth Sciences : Mathematics
The C*-algebras of certain Lie groups
Günther, Janne-Kathrin mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
University of Luxembourg, ​Luxembourg, ​​Luxembourg
Docteur en Mathématiques
Olbrich, Martin mailto
Ludwig, Jean mailto
Thalmaier, Anton mailto
Beltita, Ingrid mailto
Hilgert, Joachim mailto
Pasquale, Angela mailto
[en] C*-algebra ; Lie group ; Dual space ; Topology ; Fourier transform ; Operator fields
[en] In this doctoral thesis, the C*-algebras of the connected real two-step nilpotent Lie groups and the Lie group SL(2,R) are characterized. Furthermore, as a preparation for an analysis of its C*-algebra, the topology of the spectrum of the semidirect product U(n) x H_n is described, where H_n denotes the Heisenberg Lie group and U(n) the unitary group acting by automorphisms on H_n. For the determination of the group C*-algebras, the operator valued Fourier transform is used in order to map the respective C*-algebra into the algebra of all bounded operator fields over its spectrum. One has to find the conditions that are satisfied by the image of this C*-algebra under the Fourier transform and the aim is to characterize it through these conditions. In the present thesis, it is proved that both the C*-algebras of the connected real two-step nilpotent Lie groups and the C*-algebra of SL(2,R) fulfill the same conditions, namely the “norm controlled dual limit” conditions. Thereby, these C*-algebras are described in this work and the “norm controlled dual limit” conditions are explicitly computed in both cases. The methods used for the two-step nilpotent Lie groups and the group SL(2,R) are completely different from each other. For the two-step nilpotent Lie groups, one regards their coadjoint orbits and uses the Kirillov theory, while for the group SL(2,R) one can accomplish the calculations more directly.
Fonds National de la Recherche - FnR
The C*-algebras of certain Lie groups
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FnR ; FNR3964572 > Janne-Kathrin Gunther > > The C*-algebras of certain Lie groups > 01/11/2012 > 31/10/2016 > 2012

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