Inductive limits of projective C*-algebras. - IMAR
Inductive limits of projective C*-algebras. - IMAR
Inductive limits of projective C*-algebras. - IMAR
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Noncommutative shape theory II<br />
Definition 2.2<br />
If in the above definition, there is always a lift σ: A → C, then<br />
the morphism is called (weakly) <strong>projective</strong>.<br />
A C ∗ -algebra A is called (weakly) (semi-)<strong>projective</strong>, if the<br />
morphisms id A: A → A is.<br />
A semi<strong>projective</strong>:<br />
A σ<br />
ψ<br />
C/Jk<br />
C/ <br />
k Jk<br />
Theorem 2.3 (Blackadar)<br />
A <strong>projective</strong>:<br />
ψ<br />
A σ<br />
C<br />
C/J<br />
Every C ∗ -<strong>algebras</strong> is the inductive limit <strong>of</strong> an inductive system<br />
with semi<strong>projective</strong> connecting maps. Such a system is called<br />
shape system.<br />
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