Regular Ideals, Ideal intersections, and quotients

Document Type

Presentation Abstract

Presentation Date

9-12-2022

Abstract

Ideals in commutative C*-algebras are well understood. The study of ideals in more general C*-algebras is aided by the presence of large commutative subalgebras. We say a commutative subalgebra B of A has the ideal intersection property if every nontrivial ideal of A has nontrival intersection with B: thus reducing the study of ideals in A to the well understood commutative context. In this talk we will explore the ideal intersection property in some familiar examples such as matrix algebras and see that this property does not always pass to quotients. However, in many cases the ideal intersection property will pass to quotients by regular ideals. We will discuss regular ideals and their properties, culminating in a proof that the ideal intersection property passes to quotients by regular ideals under some mild hypotheses. This is joint work with A. Fuller, D. Pitts, and S. Reznikoff.

Additional Details

September 12, 2022 at 3:00 p.m. Math 103

This document is currently not available here.

Share

COinS