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The C*-algebras of certain Lie groups Günther, Janne-Kathrin Doctoral thesis (2016) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 227 (21 UL)The C*-algebras of real two-step nilpotent Lie groups Günther, Janne-Kathrin Speeches/Talks (2015) Using the operator valued Fourier transform, the C*-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it ... [more ▼] Using the operator valued Fourier transform, the C*-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it is shown by explicit computations, that the Fourier transform of such C*-algebras fulfills the norm controlled dual limit property. [less ▲] Detailed reference viewed: 90 (5 UL)The C*-algebras of connected real two-step nilpotent Lie groups Günther, Janne-Kathrin ; in Revista Matemática Complutense (2015) Using the operator valued Fourier transform, the C*-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it ... [more ▼] Using the operator valued Fourier transform, the C*-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it is shown by explicit computations, that the Fourier transform of such C*-algebras fulfills the norm controlled dual limit property. [less ▲] Detailed reference viewed: 148 (7 UL)The C*-algebras of connected real two-step nilpotent Lie groups Günther, Janne-Kathrin ; E-print/Working paper (2014) Using the operator valued Fourier transform, the C*-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it ... [more ▼] Using the operator valued Fourier transform, the C*-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it is shown by explicit computations, that the Fourier transform of such C*-algebras fulfills the norm controlled dual limit property. [less ▲] Detailed reference viewed: 71 (8 UL)Représentation des fonctions de réponse radiométrique ; ; et al E-print/Working paper (2013) Detailed reference viewed: 82 (7 UL) |
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