# Finite-dimensionality in the non-commutative Choquet boundary: peaking phenomena and $\mathrm{C}^*$-liminality.

@article{Clouatre2020FinitedimensionalityIT, title={Finite-dimensionality in the non-commutative Choquet boundary: peaking phenomena and \$\mathrm\{C\}^*\$-liminality.}, author={Raphael Clouatre and Ian Thompson}, journal={arXiv: Operator Algebras}, year={2020} }

We explore the finite-dimensional part of the non-commutative Choquet boundary of an operator algebra. In other words, we seek finite-dimensional boundary representations. Such representations may fail to exist even when the underlying operator algebra is finite-dimensional. Nevertheless, we exhibit mechanisms that detect when a given finite-dimensional representation lies in the Choquet boundary. Broadly speaking, our approach is topological and requires identifying isolated points in the…

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