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$C^*$-Algebra Extensions of $C(X)$

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Electronic ISBN: 978-1-4704-0129-0
Product Code: MEMO/115/550.E
List Price: $41.00 MAA Member Price:$36.90
AMS Member Price: $24.60 Click above image for expanded view$C^*$-Algebra Extensions of$C(X)$Available Formats:  Electronic ISBN: 978-1-4704-0129-0 Product Code: MEMO/115/550.E  List Price:$41.00 MAA Member Price: $36.90 AMS Member Price:$24.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1151995; 89 pp
MSC: Primary 46;

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.

Research mathematicians.

• Chapters
• Introduction
• I. Totally trivial extensions
• II. The functor $E(\cdot , A)$
• III. BDF theory for $C^*$-algebras with real rank zero
• IV. Extensions by finite matroid algebras
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Volume: 1151995; 89 pp
MSC: Primary 46;

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.

• II. The functor $E(\cdot , A)$
• III. BDF theory for $C^*$-algebras with real rank zero