Abstract
We define and study a noncommutative Fourier transform on every homogeneous complex bounded domain. We then give an application in noncommutative differential geometry by defining noncommutative Baumslag–Solitar tori.
This work was supported by the Belgian Interuniversity Attraction Pole (IAP) within the framework “Dynamics, Geometry and Statistical Physics” (DYGEST). Axel de Goursac is supported by the F.R.S.-F.N.R.S. and Florian Spinnler is supported by a F.R.I.A. fellowship (Belgium).
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Acknowledgements
One of us, Pierre Bieliavsky, spent the academic year 1995–1996 at UC Berkeley as a post-doc in the group of Professor Joseph A. Wolf. It is a great pleasure for Pierre Bieliavsky to warmly thank Professor Wolf for his support not only when a young post-doc but constantly during Pierre Bieliavsky’s career. The research presented in this note is closely related to the talk Pierre Bieliavsky gave at the West Coast Lie Theory Seminar in November 1995 when studying some early stage features of the non-formal ⋆-exponential [4].
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Bieliavsky, P., Gayral, V., de Goursac, A., Spinnler, F. (2014). Harmonic Analysis on Homogeneous Complex Bounded Domains and Noncommutative Geometry. In: Mason, G., Penkov, I., Wolf, J. (eds) Developments and Retrospectives in Lie Theory. Developments in Mathematics, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-09934-7_2
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