The stable rank of some free product C*-algebras

1996/08/09 by Ken Dykema, Dykema, Ken, Uffe Haagerup +4
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #funct-an #math.OA

paper · pdf · doi:10.48550/arxiv.funct-an/9608001

30 pages, Latex. This revision includes an extra section where the special case of the reduced C*-algebra of the free group on two generators is considered separately. This has the advantage of making the main ideas more transparent

arxiv created 1996/09/12 · arxiv updated 2009/11/30

Abstract

It is proved that the reduced group C*-algebra C*_red(G) has stable rank one (i.e. its group of invertible elements is a dense subset) if G is a discrete group arising as a free product G₁*G₂ where |G₁|>=2 and |G₂|>=3. This follows from a more general result where it is proved that if (A,tau) is the reduced free product of a family (A_i,tau_i), i∈ I, of unital C*-algebras A_i with normalized faithful traces tau_i, and if the family satisfies the Avitzour condition (i.e. the traces, tau_i, are not too lumpy in a specific sense), then A has stable rank one.

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• Simplicity and the stable rank of some free product C*-algebras
• Stable rank of C(X)\rtimesΓ
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• Stable rank one in nonnuclear crossed products
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