$K$-Continuity Is Equivalent To $K$-Exactness

Authors

  • Otgonbayar Uuye

DOI:

https://doi.org/10.7146/math.scand.a-23299

Abstract

Let $A$ be a $C^{*}$-algebra. It is well known that the functor $B \mapsto A \otimes B$ of taking the minimal tensor product with $A$ preserves inductive limits if and only if it is exact. $C^{*}$-algebras with this property play an important role in the structure and finite-dimensional approximation theory of $C^{*}$-algebras.

We consider a $K$-theoretic analogue of this result and show that the functor $B \mapsto K_{0}(A \otimes B)$ preserves inductive limits if and only if it is half-exact.

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Published

2016-03-07

How to Cite

Uuye, O. (2016). $K$-Continuity Is Equivalent To $K$-Exactness. MATHEMATICA SCANDINAVICA, 118(1), 95–105. https://doi.org/10.7146/math.scand.a-23299

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