K1-injectivity for Properly Infinite C ∗-algebras
نویسنده
چکیده
One of the main tools to classify C∗-algebras is the study of its projections and its unitaries. It was proved by Cuntz in [Cun81] that if A is a purely infinite simple C∗-algebra, then the kernel of the natural map for the unitary group U(A) to the Ktheory groupK1(A) is reduced to the connected component U(A), i.e. A isK1-injective (see §3). We study in this note a finitely generated C∗-algebra, the K1-injectivity of which would imply the K1-injectivity of all unital properly infinite C ∗-algebras. Note that such a question was already considered in [Blac07], [BRR08].
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