|
|||||
 |
|
|
|
|
|
$L^2$-Betti numbers
of rigid $C^*$-tensor categories and discrete quantum
groups
David Kyed, Sven Raum, Stefaan Vaes and Matthias Valvekens |
|
Vol. 10 (2017), No. 7, 1757–1791
|
Abstract |
|
We compute the -Betti numbers of the free -tensor categories, which are the representation categories of the universal unitary quantum groups . We show that the -Betti numbers of the dual of a compact quantum group are equal to the -Betti numbers of the representation category and thus, in particular, invariant under monoidal equivalence. As an application, we obtain several new computations of -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 -Betti number in terms of a generating set of a -tensor category. |
PDF Access Denied
However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde
We have not been able to recognize your IP address
18.208.202.194
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
$L^2$-Betti numbers, rigid $C^*$-tensor categories,
discrete quantum groups, subfactors, compact quantum groups
|
Mathematical Subject Classification 2010
Primary: 46L37
Secondary: 16E40, 18D10, 20G42
|
Milestones
Received: 9 February 2017
Revised: 3 May 2017
Accepted: 11 June 2017
Published: 1 August 2017
|
Authors |
| David Kyed | |
| Department of Mathematics and
Computer Science University of Southern Denmark DK-5230 Odense Denmark |
|
| Sven Raum | |
| Sciences de Base Section de Mathématiques École polytechnique Fédérale de Lausanne CH-1015 Lausanne Switzerland |
|
| Stefaan Vaes | |
| Department of Mathematics KU Leuven 3001 Leuven Belgium |
|
| Matthias Valvekens | |
| Department of Mathematics KU Leuven 3001 Leuven Belgium |
|
|
