{"paper":{"title":"Monoids, their boundaries, fractals and $C^\\ast$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OA"],"primary_cat":"math.AT","authors_text":"Giulia dal Verme, Thomas Weigel","submitted_at":"2019-03-12T03:59:45Z","abstract_excerpt":"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 $C^\\ast$-algebras associated to monoids. Although we must leave several important questions open, we show that the existence of self-similar M-fractals for a given monoid M, gives rise to examples of $C^\\ast$- algebras generalizing the boundary quotients discussed by X. Li in [4, {\\S}7, p. 71]. The starting point for our investigations is the observation that the universal boundary of a finitely 1-generated monoid carries na"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04716","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}