Date | 2021-03-24 |
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Speaker | Aidan Sims |

Dept. | University of Wollongong |

Room | 129-406 |

Time | 16:00-18:00 |

The notions of pure infiniteness and stable finiteness for C*-algebras were inspired by the Type decomposition of von Neumann algebras. But unlike the von Neumann case, we now know thanks to a remarkable example due to Rordam that even amongst simple, separable, nuclear C*-algebras there are examples that are neither stably finite nor purely infinite. Work of Rordam and Sierakowski (later built upon by Kirchberg and Sierakowski) showed how to investigate this dichotomy for crossed-product C*-algebras arising from group actions on the Cantor space K in terms of a “type semigroup” built from projections in C(K) modulo the relation induced by the group action. Ample groupoids generalise group actions on the Cantor set, and also incorporate constructions like inverse-semigroups, Cuntz-Krieger algebras, and partial actions. I will discuss work with Timothy Rainone on a dichotomy theorem for C*-algebras of ample groupoids using the idea of type semigroups. Very similar results were also obtained, completely independently, at almost exactly the same time by Bonicke and Li, who deserve full credit for their work.

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