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

  • Otgonbayar Uuye

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.

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
Section
Articles