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Factoriality, Connes’ type III invariants and fullness of amalgamated free product von Neumann algebras.(English)Zbl 1452.46046

Summary: We investigate factoriality, Connes’ type III invariants and fullness of arbitrary amalgamated free product von Neumann algebras using Popa’s deformation/rigidity theory. Among other things, we generalize many previous structural results on amalgamated free product von Neumann algebras and we obtain new examples of full amalgamated free product factors for which we can explicitely compute Connes’ type III invariants.

MSC:

46L10 General theory of von Neumann algebras
46L09 Free products of \(C^*\)-algebras
46L36 Classification of factors
46L55 Noncommutative dynamical systems
37A20 Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations
37A40 Nonsingular (and infinite-measure preserving) transformations

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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