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On Regularity Of Graph C*-Algebras, Gregory Joseph Faurot
On Regularity Of Graph C*-Algebras, Gregory Joseph Faurot
Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–
We prove that for any countable directed graph E with Condition (K), the corresponding graph C*-algebra C*(E) has nuclear dimension at most two. We also prove that the nuclear dimension of certain extensions is at most one, which can be applied to certain graphs to achieve the optimal upper bound of one. Finally, we generalize some previous results for O∞ -stability of graph algebras, and prove some partial results for Z-stability.
Advisor: Christopher Schafhauser
Free Semigroupoid Algebras From Categories Of Paths, Juliana Bukoski
Free Semigroupoid Algebras From Categories Of Paths, Juliana Bukoski
Department of Mathematics: Dissertations, Theses, and Student Research
Given a directed graph G, we can define a Hilbert space HG with basis indexed by the path space of the graph, then represent the vertices of the graph as projections on HG and the edges of the graph as partial isometries on HG. The weak operator topology closed algebra generated by these projections and partial isometries is called the free semigroupoid algebra for G. Kribs and Power showed that these algebras are reflexive, and that they are semisimple if and only if each path in the graph lies on a cycle. We extend …