| eBook 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 |
| eBook 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 115; 1995; 89 ppMSC: 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.
ReadershipResearch mathematicians.
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Table of Contents
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Chapters
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Introduction
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I. Totally trivial extensions
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II. The functor $E(\cdot , A)$
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III. BDF theory for $C^*$-algebras with real rank zero
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IV. Extensions by finite matroid algebras
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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
