, Volume 316, Issue 1, pp 61-82

Compressions of free products of von Neumann algebras

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Abstract.

A reduction formula for compressions of von Neumann algebra II \(_1\) –factors arising as free products is proved. This shows that the fundamental group is \({\bf R}^*_+\) for some such algebras. Additionally, by taking a sort of free product with an unbounded semicircular element, continuous one parameter groups of trace scaling automorphisms on II \(_\infty\) –factors are constructed; this produces type III \(_1\) factors with core \(\mathcal{M}\otimes B(\mathcal{H})\) , where \(\mathcal{M}\) can be a full II \(_1\) –factor without the Haagerup approximation property.

Received: 26 October 1998 / in final form 18 March 1999