The C*-algebras of connected real two-step nilpotent Lie groups

2014/09/19 by Günther, Janne-Kathrin, Ludwig, Jean
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1409.5635

Abstract

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.

Related

• C*-algebras with norm controlled dual limits and nilpotent Lie groups
• Fourier transforms of C^*-algebras of nilpotent Lie groups
• The C*-algebra of SL(2,R)
• The C^*-algebra of the group N₇.
• Fields of Toeplitz algebras for the principal symbol of regular 2-step nilpotent groups