In this note we establish some connections between the theory of self-similar fractals in the sense of John E. Hutchinson (cf. [3]), and the theory of boundary quotients of C∗-algebras associated to monoids. Although we must leave several important questions open, we show that the existence of self-similar-fractals for a given monoid, gives rise to examples of C∗-algebras (1.9) generalizing the boundary quotients Cλ∗ Cλ ∗(M) discussed by X. Li in [4, §7, p. 71]. The starting point for our investigations is the observation that the universal boundary of a finitely 1-generated monoid carries naturally two topologies. The fine topology plays a prominent role in the construction of these boundary quotients, while the cone topology can be used to define canonical measures on the attractor of an-fractal for a finitely 1-generated monoid.

Dal Verme, G., Weigel, T. (2020). Monoids, their boundaries, fractals, and C*-algebras. TOPOLOGICAL ALGEBRA AND ITS APPLICATIONS, 8(1), 28-45 [10.1515/taa-2020-0003].

Monoids, their boundaries, fractals, and C*-algebras

Dal Verme, G;Weigel, T
Membro del Collaboration Group
2020

Abstract

In this note we establish some connections between the theory of self-similar fractals in the sense of John E. Hutchinson (cf. [3]), and the theory of boundary quotients of C∗-algebras associated to monoids. Although we must leave several important questions open, we show that the existence of self-similar-fractals for a given monoid, gives rise to examples of C∗-algebras (1.9) generalizing the boundary quotients Cλ∗ Cλ ∗(M) discussed by X. Li in [4, §7, p. 71]. The starting point for our investigations is the observation that the universal boundary of a finitely 1-generated monoid carries naturally two topologies. The fine topology plays a prominent role in the construction of these boundary quotients, while the cone topology can be used to define canonical measures on the attractor of an-fractal for a finitely 1-generated monoid.
Articolo in rivista - Articolo scientifico
boundaries; C-algebras; fractals; Monoids;
English
5-mar-2020
2020
8
1
28
45
open
Dal Verme, G., Weigel, T. (2020). Monoids, their boundaries, fractals, and C*-algebras. TOPOLOGICAL ALGEBRA AND ITS APPLICATIONS, 8(1), 28-45 [10.1515/taa-2020-0003].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/298931
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