**Memoirs of the American Mathematical Society**

1995;
89 pp;
Softcover

MSC: Primary 46;

Print ISBN: 978-0-8218-2611-9

Product Code: MEMO/115/550

List Price: $41.00

Individual Member Price: $24.60

**Electronic ISBN: 978-1-4704-0129-0
Product Code: MEMO/115/550.E**

List Price: $41.00

Individual Member Price: $24.60

# \(C^{*}\)-Algebra Extensions of \(C(X)\)

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*Huaxin Lin*

This work shows that the Weyl-von Neumann theorem for unitaries holds for \(\sigma\)-unital \(AF\)-algebras and their multiplier algebras. Lin studies \(E(X,A)\), the quotient of \(\mathrm{{\mathbf{Ext}}}^{eu}_s(C(X),A)\) by a special class of trivial extension, dubbed totally trivial extensions. This leads to a BDF-type classification for extensions of \(C(X)\) by a \(\sigma\)-unital purely infinite simple \(C^*\)-algebra with trivial \(K_1\)-group. Lin also shows that, when \(X\) is a compact subset of the plane, every extension of \(C(X)\) by a finite matroid \(C^*\)-algebra is totally trivial. Classification of these extensions for nice spaces is given, as are some other versions of the Weyl-von Neumann-Berg theorem.

#### Readership

Research mathematicians.