Explicit Rieffel induction modules for quantum groups

DOI10.4171/JNCG/477arXiv1911.01779WikidataQ114021463 ScholiaQ114021463MaRDI QIDQ6328557

Damien Rivet

Publication date: 5 November 2019

Abstract: For $mathbbG$ an algebraic (or more generally, a bornological) quantum group and $mathbbB$ a closed quantum subgroup of $mathbbG$, we build in this paper an induction module by explicitly defining an inner product which takes its value in the convolution algebra of $mathbbB$, as in the original approach of Rieffel cite{Rieffel}. In this context, we study the link with the induction functor defined by Vaes. In the last part we illustrate our result with parabolic induction of complex semi-simple quantum groups with the approach suggested by Clare cite{Clare}cite{CCH}.

Mathematics Subject Classification ID

Noncommutative measure and integration (46L51) Quantum groups (quantized function algebras) and their representations (20G42) Quantizations, deformations for selfadjoint operator algebras (46L65) Hopf algebras and their applications (16T05)

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