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arXiv · 2307.12878

Quantum $SU(3)$ as the $C^*$-algebra of a 2-graph

Olof Giselsson
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Abstract

We show that for $q\in (0,1),$ the $C^{*}$-algebra $SU_{q}(3)$ is isomorphic a rank $2$ graph $C^{*}$-algebra (in the sense of Pask and Kumjian). This graph is derived by passing the to the limit $q\to 0$ for a set of generators of $SU_{q}(3)$. Moreover, the isomorphism can be taken to be $\mathbb{T}^{2}$-equivariant with respect the right-action on $SU_{q}(3)$ and the gauge action coming from the $2$-graph

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Olof Giselsson. 2023-07-24. Quantum $SU(3)$ as the $C^*$-algebra of a 2-graph. https://arxiv.org/abs/2307.12878

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