K-Theory of C*-Algebras

Lecturer: Prof. Dr. Moritz Weber
Assistant: Luca Junk

Content

In this lecture, we will introduce K-theory for C*-algebras. This is a theory of invariants for C*-algebras
with a homological flavour. More concretely, to any C*-algebra A we assign an abelian group K₀(A)
which somehow "counts the projections", as well as an abelian group K₁(A) which somehow "count
s the unitaries". Almost more important than the definition of the K-groups are the homological
properties of the K functor: it preserves many natural constructions making it much simpler to
compute the K-groups in concrete cases.

See also winter term 2019/2020 for a previous variant of this lecture.

Participants should know the definition and some basics on C*-algebras as well as functional analysis.

References

• Rordam, Mikael; Larsen, Flemming; Laustsen, Niels, An introduction to K-theory for C*-algebras, 2000.
• Blackadar, Bruce, K-theory for operator algebras, 1998.
• Wegge-Olsen, Niels, K-theory and C*-algebras. A friendly approach, 1993.
• Blackadar, Bruce, Operator algebras. Theory of C*-algebras and von Neumann algebras, 2006.
• Brown, Nathanial; Ozawa, Narutaka, C*-algebras and finite-dimensional approximations, 2008.
• Davidson, Kenneth, C*-algebras by example, 1996.
• Lecture notes by Christian Voigt

You can find these references in the library.