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arXiv · 1712.09386

On the geometry of idempotents in von Neumann algebras

Thierry Giordano·Adam Sierakowski
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Abstract

We consider the general linear group as an invariant of von Neumann factors. We prove that up to complement, a set consisting of all idempotents generating the same right ideal admits a characterisation in terms of properties of the general linear group of a von Neumann factor. We prove that for two Neumann factors, any bijection of their general linear groups induces a bijection of their idempotents with the following additional property: If two idempotents or their two complements generate the same right ideal, then so does their image. This generalises work on regular rings, such include von Neumann factors of type $I_{n}$, $n < \infty$.

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Thierry Giordano, Adam Sierakowski. 2017-12-26. On the geometry of idempotents in von Neumann algebras. https://arxiv.org/abs/1712.09386

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