Abstract
Can a group be recovered from its representation theory? That is the question we discuss in these lecture notes, with focus on Lie groups. By representation theory of a group we mean not only its representations but also their mutual relations, in a sense that still remains to be specified. To this end we try to extend the group representations to representations of some kind of enveloping associative algebra of the group under consideration, specifically, the group C∗-algebra. In particular, we look for topologies on various sets of representations, in order to make precise the idea that some representations are close to each other.
This research was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI—UEFISCDI, project number PN-III-P4-ID-PCE-2020-0878, within PNCDI III.
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Beltiţă, D. (2023). Lecture Notes on Quantization and Group C∗-Algebras. In: Kielanowski, P., Dobrogowska, A., Goldin, G.A., Goliński, T. (eds) Geometric Methods in Physics XXXIX. WGMP 2022. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-30284-8_26
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DOI: https://doi.org/10.1007/978-3-031-30284-8_26
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