Infinite alphabet edge shift spaces via ultragraphs and their C*-algebras
By D. Gonccalves, D. Royer. 2017
48 citations recorded by the source corpus.
We define a notion of (one-sided) edge shift spaces associated to ultragraphs. In the finite case our notion coincides with the edge shift space of a graph. In general, we show that our space is metrizable and has a countable basis of clopen sets. We show that for a large class of ultragraphs the basis elements of the topology are compact. We examine shift morphisms between these shift spaces, and, for the locally compact case, show that if two (possibly infinite) ultragraphs have edge shifts that are conjugate, via a conjugacy that preserves length, then the associated ultragraph C*-algebras are isomorphic. To prove this last result we realize the relevant ultragraph C*-algebras as partial crossed products.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fea482e9b7a10cd7a386fa2aaff544adec17b342
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Recent developments around partial actions (2018, background): “Moreover, partial crossed products turned out to be useful to deal with C-algebras arising from self-similar graph actions in [162], with C-algebras associated to any stationary ordered Bratteli diagram in [185], as well as with ultragraph C-algebras and related infinite alphabet shifts in [187], [1”