An L²-Kunneth formula for tracial algebras

2009/03/05 by David Kyed, Kyed, David
Mathematics · #16E30 #16W30 #46L89 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0903.0931

openalex publication_date 2009/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a Kunneth formula computing the Connes-Shlyakhtenko L²-Betti numbers of the algebraic tensor product of two tracial *-algebras in terms of the L²-Betti numbers of the two original algebras. As an application, we construct examples of non-finite, non-cocommutative, compact quantum groups with a non-vanishing first L²-Betti number.

Related

• On the l²-Betti numbers of universal quantum groups
• On the zeroth L²-homology of a quantum group
• Higher l²-Betti numbers of universal quantum groups
• L²-Betti numbers of coamenable quantum groups
• L²-Betti numbers for subfactors