A Tensor Product for Representations of the Cuntz Algebra and of the R. Thompson Groups

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2025年5月28日

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Arnaud Brothier,
Dilshan Wijesena

摘要

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 $\mathcal {O}$ $O$ and conversely all representations of $\mathcal {O}$ $O$ are of this form. Via this approach we introduce a tensor product for a large class of representations of $F,T,V,\mathcal {O}$ $F, T, V, O$ . We prove that a sub-category forms a tensor category and perform a number of explicit computations of fusion rules.