@prefix vivo: . @prefix edm: . @prefix dcterms: . @prefix dc: . @prefix skos: . @prefix ns0: . vivo:departmentOrSchool "Non UBC"@en ; edm:dataProvider "DSpace"@en ; dcterms:creator "Castillo-Ramirez, Alonso"@en ; dcterms:issued "2019-11-13T11:06:08Z"@en, "2019-05-16T09:00"@en ; dcterms:description """

For any group $G$ and set $A$, let $\\text{CA}(G;A)$ be the monoid of all cellular automata over the configuration space $A^G$. In this talk, we present some algebraic results on $\\text{CA}(G;A)$ when $G$ and $A$ are both finite. First, we show that any generating set of $\\text{CA}(G;A)$ must have a cellular automaton with minimal memory set equal to $G$ itself. Second, we describe the structure of the group of units of $\\text{CA}(G;A)$ in terms of a set of representatives of the conjugacy classes of subgroups of $G$. Third, we discuss the minimal cardinality of a generating set of $\\text{CA}(G;A)$: in some cases we give it precisely, while in others we give some bounds. We apply this to provide a simple proof that $\\text{CA}(G;A)$ is not finitely generated for various kinds of infinite groups $G$."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/72262?expand=metadata"@en ; dcterms:extent "39.0 minutes"@en ; dc:format "video/mp4"@en ; skos:note ""@en, "Author affiliation: Universidad de Guadalajara"@en ; edm:isShownAt "10.14288/1.0385174"@en ; dcterms:language "eng"@en ; ns0:peerReviewStatus "Unreviewed"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ; ns0:scholarLevel "Faculty"@en ; dcterms:isPartOf "BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))"@en ; dcterms:subject "Mathematics"@en, "Dynamical systems and ergodic theory"@en, "Group theory and generalizations"@en, "Dynamical systems"@en ; dcterms:title "Generating sets of monoids of cellular automata"@en ; dcterms:type "Moving Image"@en ; ns0:identifierURI "http://hdl.handle.net/2429/72262"@en .