Boundary $C^*$-algebras of triangle geometries

Guyan Robertson

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arXiv · 1308.0908

Boundary $C^*$-algebras of triangle geometries

Guyan Robertson

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Abstract

Let $\Delta$ be a building of type $\widetilde A_2$ and order $q$, with maximal boundary $\Omega$. Let $\Gamma$ be a group of type preserving automorphisms of $\Delta$ which acts regularly on the chambers of $\Delta$. Then the crossed product $C^*$-algebra $C(\Omega) \rtimes \Gamma$ is isomorphic to $M_{3(q+1)} \otimes\cl O_{q^2}\otimes\cl O_{q^2}$, where $\cl O_n$ denotes the Cuntz algebra generated by $n$ isometries whose range projections sum to the identity operator.

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BibTeX RIS

Guyan Robertson. 2013-08-05. Boundary $C^*$-algebras of triangle geometries. https://arxiv.org/abs/1308.0908

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