L 2-betti numbers of rigid C*-tensor categories and discrete quantum groups

David Kyed, Sven Raum, Stefaan Vaes, Matthias Valvekens

Research output: Contribution to journalJournal articleResearchpeer-review

218 Downloads (Pure)

Abstract

We compute the L 2-Betti numbers of the free C *-tensor categories, which are the representation categories of the universal unitary quantum groups A u(F). We show that the L 2-Betti numbers of the dual of a compact quantum group G(double-struck) are equal to the L 2-Betti numbers of the representation category Rep(G(double-struck)) and thus, in particular, invariant under monoidal equivalence. As an application, we obtain several new computations of L 2-Betti numbers for discrete quantum groups, including the quantum permutation groups and the free wreath product groups. Finally, we obtain upper bounds for the first L 2-Betti number in terms of a generating set of a C *-tensor category.

Original languageEnglish
JournalAnalysis & PDE
Volume10
Issue number7
Pages (from-to)1757-1791
ISSN2157-5045
DOIs
Publication statusPublished - 2017

Keywords

  • Compact quantum groups
  • Discrete quantum groups
  • L -Betti numbers
  • Rigid C -tensor categories
  • Subfactors

Fingerprint

Dive into the research topics of 'L 2-betti numbers of rigid C*-tensor categories and discrete quantum groups'. Together they form a unique fingerprint.

Cite this