Mathematics – Operator Algebras
Scientific paper
2008-04-29
Mathematics
Operator Algebras
Quanta of Maths (Clay Math. Institute), 48--54
Scientific paper
One of the main tools to classify \cst-algebras is the study of its projections and its unitaries. It was proved by Cuntz in \cite{Cu81} that if $A$ is a \textit{purely infinite} simple \cst-algebra, then the kernel of the natural map for the unitary group $\U(A)$ to the $K$-theory group $K_1(A)$ is reduced to the connected component $\U^0(A)$, i.e. $A$ is \textit{$K_1$-injective} (see \S 3). We study in this note a finitely generated \cst-algebra, the $K_1$-injectivity of which would imply the $K_1$-injectivity of all unital \textit{properly infinite} \cst-algebras.
No associations
LandOfFree
K_1-injectivity for properly infinite C*-algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with K_1-injectivity for properly infinite C*-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and K_1-injectivity for properly infinite C*-algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-210056