On the von Neumann algebras associated to Yang–Baxter operators

Bożejko and Speicher associated a finite von Neumann algebra MT to a self-adjoint operator T on a complex Hilbert space of the form $\mathcal {H}\otimes \mathcal {H}$ which satisfies the Yang–Baxter relation and $ \left\| T \right\| < 1$. We show that if dim$(\mathcal {H})$ ⩾ 2, then MT is a fact...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2021-08, Vol.151 (4), p.1331-1354
Main Authors: Bikram, Panchugopal, Kumar, Rahul, Mohanta, Rajeeb, Mukherjee, Kunal, Saha, Diptesh
Format: Article
Language:English
Subjects:
Algebra
Construction
Eigenvectors
Generators
Hilbert space
Investigations
Operators (mathematics)
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Summary:Bożejko and Speicher associated a finite von Neumann algebra MT to a self-adjoint operator T on a complex Hilbert space of the form $\mathcal {H}\otimes \mathcal {H}$ which satisfies the Yang–Baxter relation and $ \left\| T \right\| < 1$. We show that if dim$(\mathcal {H})$ ⩾ 2, then MT is a factor when T admits an eigenvector of some special form.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2020.62