C*-algebras of labelled spaces and their diagonal C*-subalgebras

Giuliano Boava; Gilles G. de Castro; Fernando de L. Mortari

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arXiv · 1605.06460

C-algebras of labelled spaces and their diagonal C-subalgebras

Giuliano Boava·Gilles G. de Castro·Fernando de L. Mortari

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Abstract

Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space, inspired by how one might cut or glue labelled paths together, that proves that non-zero elements in the inverse semigroup correspond to non-zero elements in the C*-algebra. We also show that the spectrum of its diagonal C*-subalgebra is homeomorphic to the tight spectrum of the inverse semigroup associated with the labelled space.

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Giuliano Boava, Gilles G. de Castro, Fernando de L. Mortari. 2016-05-20. C*-algebras of labelled spaces and their diagonal C*-subalgebras. https://arxiv.org/abs/1605.06460

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