On the classification of free Bogoljubov crossed product von Neumann algebras by the integers

  • Sven Raum

    Westfälische Wilhelms-Universität Münster, Germany

Abstract

We consider crossed product von Neumann algebras arising from free Bogoljubov actions of Z\mathbb Z. We describe several presentations of them as amalgamated free products and cocycle crossed products and give a criterion for factoriality. A number of isomorphism results for free Bogoljubov crossed products are proved, focusing on those arising from almost periodic representations. We complement our isomorphism results by rigidity results yielding non-isomorphic free Bogoljubov crossed products and by a partial characterisation of strong solidity of a free Bogoljubov crossed products in terms of properties of the orthogonal representation from which it is constructed.

Cite this article

Sven Raum, On the classification of free Bogoljubov crossed product von Neumann algebras by the integers. Groups Geom. Dyn. 8 (2014), no. 4, pp. 1207–1245

DOI 10.4171/GGD/301