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Award ID contains: 1900916

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  1. ; ; ; ; (, Advances in Mathematics)
    Full Text Available 
  2. ; (, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)
    Abstract In this paper we show that every non-cycle finite transitive directed graph has a Cuntz–Krieger family whose WOT-closed algebra is $$B(\mathcal {H})$$ . This is accomplished through a new construction that reduces this problem to in-degree 2-regular graphs, which is then treated by applying the periodic Road Colouring Theorem of Béal and Perrin. As a consequence we show that finite disjoint unions of finite transitive directed graphs are exactly those finite graphs which admit self-adjoint free semigroupoid algebras. 
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  3. (, Documenta mathematica)
    We study quotients of the Toeplitz C*-algebra of a random walk, similar to those studied by the author and Markiewicz for finite stochastic matrices. We introduce a new Cuntz-type quotient C*-algebra for random walks that have convergent ratios of transition probabilities. These C*-algebras give rise to new notions of ratio limit space and boundary for such random walks, which are computed by appealing to a companion paper by Woess. Our combined results are leveraged to identify a unique symmetry-equivariant quotient C*-algebra for any symmetric random walk on a hyperbolic group, shedding light on a question of Viselter on C*-algebras of subproduct systems. 
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    Accepted Manuscript Full Text Available
  4. (, Compositio mathematica)
    null (Ed.)
    Accepted Manuscript Full Text Available
  5. ; ; ; ; (, Journal of Noncommutative Geometry)
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