# Journal of Operator Theory

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

An $L^2$-Kunneth formula for tracial algebras**Authors**: David Kyed

**Author institution:**Mathematisches Institut, Georg-August-Universitaet Goettingen, Bunsenstrasse 3-5, D-37073 Goettingen, Germany

**Summary:**We prove a Künneth formula computing the Connes-Shlyakhtenko $L^2$-Betti numbers of the algebraic tensor product of two tracial $*$-algebras 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.

**Keywords:**$L^2$-Betti numbers, Künneth formula, quantum groups

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