On the classification of free Bogoljubov crossed product von Neumann algebras by the integers (Q2264083)
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| Language | Label | Description | Also known as |
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| English | On the classification of free Bogoljubov crossed product von Neumann algebras by the integers |
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On the classification of free Bogoljubov crossed product von Neumann algebras by the integers (English)
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20 March 2015
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Summary: 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.
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free Gaussian functor
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deformation/rigidity theory
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\(\mathrm{II}_1\) factors
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free Bogoljubov actions
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Bogoljubov crossed product
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