Non-stable K-theory and extremally rich C*-algebras

Lawrence G. Brown; Gert K. Pedersen

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arXiv · 0708.3078

Non-stable K-theory and extremally rich C*-algebras

Lawrence G. Brown·Gert K. Pedersen

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Abstract

We consider the properties weak cancellation, K_1-surjectivity, good index theory, and K_1-injectivity for the class of extremally rich C*-algebras, and for the smaller class of isometrically rich C*-algebras. We establish all four properties for isometrically rich C*-algebras and for extremally rich C*-algebras that are either purely infinite or of real rank zero, K_1-injectivity in the real rank zero case following from a prior result of H. Lin. We also show that weak cancellation implies the other properties for extremally rich C*-algebras and that the class of extremally rich C*-algebras with weak cancellation is closed under extensions. Moreover, we consider analogous properties which replace the group K_1(A) with the extremal K-set K_e(A) as well as two versions of K_0-surjectivity.

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BibTeX RIS

Lawrence G. Brown, Gert K. Pedersen. 2014-04-03. Non-stable K-theory and extremally rich C*-algebras. https://arxiv.org/abs/0708.3078

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