Simplicity of Crossed Products of C*-algebras

Specialeforsvar ved Malthe Munk Karbo

Titel: Simplicity of Crossed Products of C*-algebras

Abstract:

The classification theory of C*-algebras is vast and quite developed. In recent years, new developments has been made in the field working with the classification of C*-simple groups, in particular following the release of [KK14]. These papers relied on the classification theory of certain C*-algebras associated to a C*-dynamical system which are called crossed products. The crossed product construction is not new and it provide interesting examples of non-trivial C*-algebras, such as irrational rotation algebras. However, it is not easy to describe the ideal structure of crossed products for arbitrary groups G and C*-algebras. In this thesis, we examine both the construction of the general crossed products as well as a subsample of available variants. We then examine conditions which allows us to describe their ideal structure, and we end this thesis by applying the theory examined to prove the main result of [KK14].

Vejleder:  Søren Eilers
Censor:    Wojciech Szymanski, SDU