Some Dimension Theories of C*-algebras and Rokhlin-type Properties

Abstract: There are many ranks associated with a $C^*$-algebra. Rieffel defined the notion of stable ranks in the 1980s. We will mainly focus on two of these ranks namely connected stable rank and general stable rank. If we are given a group $G$, which acts on a $C^*$-algebra $A$ via a map $\alpha$, the triple $(A, G, \alpha)$ is said to be a $C^*$-dynamical system, then we can associate a $C^*$-algebra called a crossed product $C^*$-algebra denoted by $A \rtimes_{\alpha}G$. We will discuss the homotopical stable ranks of a crossed product $C^*$-algebra by a finite group where the action involved has Rokhlin-type property.

functional analysisK-theory and homologyoperator algebras

Audience: researchers in the topic

Webinars on Operator Theory and Operator Algebras