MATH 488/489: Astrid an Huef's Projects

 

Unitisations of C*-algebras associated to groupoids

A C*-algebra A is an algebra of operators on Hilbert space, and is called unital if it has an identity: an element 1 in A such that 1a=a=a1 for all elements a of A. There are several ways to adjoin an identity to a nonunital C*-algebra. Here we will study adjoining an identity to a C*-algebra associated to a mathematical object called a groupoid, a generalisations of a group which has many identities and only a partially defined operation. The groupoids of this project arise from actions of groups on spaces and from directed graphs.