Electronic ISBN:  9781470401290 
Product Code:  MEMO/115/550.E 
List Price:  $41.00 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 115; 1995; 89 ppMSC: Primary 46;
This work shows that the Weylvon 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 BDFtype 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 Weylvon NeumannBerg theorem.
ReadershipResearch mathematicians.

Table of Contents

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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This work shows that the Weylvon 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 BDFtype 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 Weylvon NeumannBerg 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