Journal of Operator Theory

Volume 67, Issue 2, Spring 2012 pp. 317-327.

$L^2$ -Kunneth formula for tracial algebras

Authors: David Kyed
Author institution: Mathematisches Institut, Georg-August-Universitaet Goetting\-en, Bunsenstrasse 3-5, D-37073 Goettingen, Germany

Summary: We prove a K{\"u}nneth formula computing the Connes--Shlyakh\-tenko

$L^2$ -Betti numbers of the algebraic tensor product of two tracial

$*$ -alge\-bras in terms of the

$L^2$ -Betti numbers of the two original algebras. As an application, we construct examples of compact quantum groups with a non-vanishing first

$L^2$ -Betti number.

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