C*-equivalences of k-graph and N-graph Algebras Through Graph Transformations

dc.contributor.authorListhartke, Benjamin
dc.date.accessioned2024-04-15T18:55:48Z
dc.date.available2024-04-15T18:55:48Z
dc.date.graduationmonthMay
dc.date.published2024
dc.description.abstractIn the study of operator algebras, C*-algebras act as a generalization of matrix algebras over a vector space. A rich source of C*-algebras to study is the graph algebra, where functions are chosen based on the vertices and edges of a directed graph. Eilers and Ruiz proved in 2019 that many transformations of the graph—insplits, outsplits, and others—do not affect the ideal structure of the graph algebra. In 2020, several of these transformations of k-graphs (a higher-rank analog of directed graphs) were also shown to preserve Morita equivalence but the outsplit is missing from this list. We expand on this previous work by showing that the outsplit of a higher-rank graph will preserve Morita equivalence as well. We then begin to elevate this discussion to N-graph algebras by showing that sink deletion, delay, and reduction also preserve Morita equivalence.
dc.description.advisorSarah Reznikoff
dc.description.degreeDoctor of Philosophy
dc.description.departmentDepartment of Mathematics
dc.description.levelDoctoral
dc.identifier.urihttps://hdl.handle.net/2097/44303
dc.language.isoen_US
dc.subjectOperator Algebras, C*-algebras, graph algebras, directed graphs, higher rank graphs
dc.titleC*-equivalences of k-graph and N-graph Algebras Through Graph Transformations
dc.typeDissertation

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