Ring C*-algebras

2009/05/29 by Li, Xin
#11R04 #11R56 #16-xx (Secondary) #46L05 (Primary) #58B34 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0905.4861

Abstract

We associate reduced and full C*-algebras to arbitrary rings and study the inner structure of these ring C*-algebras. As a result, we obtain conditions for them to be purely infinite and simple. We also discuss several examples. Originially, our motivation comes from algebraic number theory.

Related

• Structure of non-unital purely infinite simple rings
• A properly infinite C*-algebra which is not K₁-injective
• K₀ of purely infinite simple regular rings
• Selfless C*-algebras
• Remarks on computing the Grothendieck rings of C*-algebras