College of Liberal Arts & Sciences

# Operator Therory Seminar - Professor Kathryn McCormick; Math & Statistics; California State University Long Beach "Holomorphic subalgebras of $n$-homogeneous $C^*$-algebras"

Operator Theory - Tuesdays

1:30-2:30 Zoom ID 941 8109 7364

Professor Kathryn McCormick

Math & Statistics

California State University Long Beach

Title: "Holomorphic subalgebras of $n$-homogeneous $C^*$-algebras"

Abstract: There is a long tradition of analyzing a $C^*$-algebra through some topological invariant. One such result is Tomiyama and Takesaki's 1961 proof that an $n$-homogeneous $C^*$-algebra $A$ is determined up to $*$-isomorphism by an underlying continuous matrix bundle, and $A$ is an algebra of continuous cross-sections of the bundle. Suppose that the base space of the bundle is a bordered Riemann surface with finitely many smooth boundary components. Then for each such $n$-homogeneous $C^*$-algebra, one can define a subalgebra of holomorphic cross-sections. We will describe a partial result towards classifying these subalgebras up to complete isometric isomorphism based on topological invariants.