Groups, Geometry, and Dynamics


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Volume 8, Issue 4, 2014, pp. 1207–1245
DOI: 10.4171/GGD/301

Published online: 2014-12-31

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

Sven Raum[1]

(1) Westfälische Wilhelms-Universität Münster, Germany

We consider crossed product von Neumann algebras arising from free Bogoljubov actions of $\mathbb Z$. 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.

Keywords: Free Gaussian functor, deformation/rigidity theory, II$_1$ factors

Raum Sven: On the classification of free Bogoljubov crossed product von Neumann algebras by the integers. Groups Geom. Dyn. 8 (2014), 1207-1245. doi: 10.4171/GGD/301