Groups, Geometry, and Dynamics
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Published online: 2014-12-31
On the classification of free Bogoljubov crossed product von Neumann algebras by the integersSven Raum (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