C*-algebras and self-similar groups

By Volodymyr V. Nekrashevych. 2009

102 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/52fb566dc94b3b700b5a6ef62161b72c8ae160e0

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In Algebra and Number Theory

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Citations in the corpus

On C*-algebras associated to right LCM semigroups (2014, background): “The CuntzPimsner algebra O(G,X) of a self-similar group has been studied in [23, 25], and the Toeplitz algebra T (G,X) has been studied in [13].”
Zappa-Sz\'ep products of semigroups and their C*-algebras (2013, background): “A seemingly unrelated class of C-algebras has recently been discovered by Nekrashevych [22, 24], namely those associated with self-similar group actions.”
Simplicity of algebras associated to non-Hausdorff groupoids (2018, background): “In [21], Nekrashevych associates a C*-algebra to (G,X), denoted OG,X , which is the universal C*-algebra generated by a set of isometries {sx}x∈X and a unitary representation {ug}g∈G satisfying (i) sxsy = 0 if x 6= y, (ii) ∑ x∈X sxs ∗ x = 1 and (iii) ugsx = sg·xug|x .”
Boundary quotients of C*-algebras of right LCM semigroups (2014, background): “,α) → g·α, such that for all g∈ G, x∈ X there exists a unique element of G, denoted g|x, such that for all α∈ X∗ g(xα) = (g·x)(g|x ·α). In this case, the pair (G,X) is called a self-similar group. In [Nek09], Nekrashevych associates a C*-algebra to (G,X), denoted OG,X, which is the universal C*-alge”
The tight groupoid of an inverse semigroup (2014, methodology): “To mention an example of interest to us, in [6] and [7] a unified treatment was given to a certain class of C*-algebras studied by Katsura in [9], alongside Nekrashevych’s C*algebras introduced and discussed in [12], [13] and [14].”
Self-similar graphs, a unified treatment of Katsura and Nekrashevych C*-algebras (2014, methodology): “We would like to stress that, like Nekrashevych’s groupoid [26: Theorem 5.1], our groupoid GG,E is constructed as a groupoid of germs.”