Nonstable K--theory for extension algebras of the simple purely infinite C^*--algebra by certain C^*--algebras

2010/06/29 by Zhihua Li, Li, Zhihua, Yifeng Xue +1
Mathematics · #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1006.5725

openalex publication_date 2010/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let 0\longrightarrow \B\stackrelj\longrightarrowE\stackrelπ\longrightarrow\A\longrightarrow 0 be an extension of \A by \B, where \A is a unital simple purely infinite C^*--algebra. When \B is a simple separable essential ideal of the unital C^*--algebra E with \RR(\B)=0 and \rm(PC), K₀(E)=\[p]| p is a projection in E∖ B\; When B is a stable C^*--algebra, \U(C(X,E))/\U₀(C(X,E))≅ K₁(C(X,E)) for any compact Hausdorff space X.

Related

• Extensions of C*-algebras
• The K-Theory of a Simple Separable Exact C*-Algebra Not Isomorphic to Its Opposite Algebra
• Purely infinite simple C^*-algebras arising from free product constructions
• Nonstable K-theory for Z-stable C*-algebras
• E-theory is a special case of KK-theory