# Reference Request: Group C* Algebra

Currently I am finishing the reference called "C* Algebra By Example" written by Kenneth Davidson and looking for another reference related to Group C* Algebra. I tried to read the "C* Algebras and Operator Theory" written by Gerard Murray but found out that this book only focuses on representations. I used the lecture notes written by Lan Putnam before, which cover quite a number of topics in C* Algebra but does not contain that many details.

Could anyone share some of the reference you used or liked if you have ever studied Group C* Algebra? Ideally your reference will cover C* Algebra on a locally compact group or free group (e.g. $$\mathbb{F}_{2}$$).

The flavor of the continuous case is also much more classical, while for discrete groups there are many topics that are currently (or recently) active (approximation properties, Kazhdan property for $$C^\ast$$-algebras, $$C^\ast$$-simplicity, etc)
• Dixmier, Jacques, $$C^*$$-algebras. North-Holland Mathematical Library. Vol. 15. Amsterdam (1977). ZBL0372.46058. Dixmier book has a few chapters dedicated to group algebras.
• Brown, Nathanial P.; Ozawa, Narutaka, $$C^*$$-algebras and finite-dimensional approximations, Graduate Studies in Mathematics (2008). ZBL1160.46001. Chapters !2 and 15.