A tensor product for representations of the Cuntz algebra and of the R. Thompson groups

Arnaud Brothier; Dilshan Wijesena

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arXiv · 2408.12051

A tensor product for representations of the Cuntz algebra and of the R. Thompson groups

Arnaud Brothier·Dilshan Wijesena

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Abstract

The authors continue a series of articles studying certain unitary representations of the Richard Thompson groups $F,T,V$ called Pythagorean. They all extend to the Cuntz algebra $\mathcal{O}$ and conversely all representations of $\mathcal{O}$ are of this form. Via this approach we introduce a tensor product for a large class of representations of $F,T,V,\mathcal{O}$. We prove that a sub-category forms a tensor category and perform a number of explicit computations of fusion rules.

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Arnaud Brothier, Dilshan Wijesena. 2024-08-22. A tensor product for representations of the Cuntz algebra and of the R. Thompson groups. https://arxiv.org/abs/2408.12051

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