English

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

Operator Algebras 2023-10-24 v2 Quantum Algebra

Abstract

We show that for q(0,1),q\in (0,1), the CC^{*}-algebra SUq(3)SU_{q}(3) is isomorphic a rank 22 graph CC^{*}-algebra (in the sense of Pask and Kumjian). This graph is derived by passing the to the limit q0q\to 0 for a set of generators of SUq(3)SU_{q}(3). Moreover, the isomorphism can be taken to be T2\mathbb{T}^{2}-equivariant with respect the right-action on SUq(3)SU_{q}(3) and the gauge action coming from the 22-graph

Keywords

Cite

@article{arxiv.2307.12878,
  title  = {Quantum $SU(3)$ as the $C^*$-algebra of a 2-graph},
  author = {Olof Giselsson},
  journal= {arXiv preprint arXiv:2307.12878},
  year   = {2023}
}