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.
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Received: 26 October 1998 / in final form 18 March 1999
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Dykema, K., Radulescu, F. Compressions of free products of von Neumann algebras. Math Ann 316, 61–82 (2000). https://doi.org/10.1007/s002080050004
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DOI: https://doi.org/10.1007/s002080050004