AMS Bookstore LOGO amslogo
AMS TextbooksAMS Applications-related Books
\(C^*\)-Algebra Extensions of \(C(X)\)
Huaxin Lin

Memoirs of the American Mathematical Society
1995; 89 pp; softcover
Volume: 115
ISBN-10: 0-8218-2611-5
ISBN-13: 978-0-8218-2611-9
List Price: US$41
Individual Members: US$24.60
Institutional Members: US$32.80
Order Code: MEMO/115/550
[Add Item]

Request Permissions

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.

Table of Contents

  • Introduction
  • Totally trivial extensions
  • The functor \(E(\cdot \,, A)\)
  • BDF theory for \(C^*\)-algebras with real rank zero
  • Extensions by finite matroid algebras
  • References
Powered by MathJax

  AMS Home | Comments:
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia