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

Abstract

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.