An L^2-Kunneth formula for tracial algebras

TL;DR

This paper establishes a Kunneth formula for L^2-Betti numbers of tensor products of tracial *-algebras, enabling new computations and applications in quantum group theory.

Contribution

It introduces a novel Kunneth formula for L^2-Betti numbers of tracial *-algebras, expanding tools for quantum algebra analysis.

Findings

Derived a formula for L^2-Betti numbers of tensor products

Constructed examples of quantum groups with non-zero first L^2-Betti number

Extended understanding of quantum group invariants

Abstract

We prove a Kunneth 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 non-finite, non-cocommutative, compact quantum groups with a non-vanishing first L^2-Betti number.