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The Group of Unital C*-extensions

  • Vladimir Manuilov
  • Klaus Thomsen
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

Let A and B be separable C*-algebras, A unital and B stable. It is shown that there is a natural six-terms exact sequence which relates the group which arises by considering all semi-split extensions of A by B to the group which arises by restricting the attention to unital semi-split extensions of A by B. The six-terms exact sequence is an unpublished result of G. Skandalis.

Keywords

C*-algebra extension unital extension absorbing homomorphism 

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References

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    W. Arveson, Notes on extensions of C*-algebras. Duke Math. J. 44 (1977), 329–355.zbMATHMathSciNetCrossRefGoogle Scholar
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    J. Cuntz and N. Higson, Kuiper’s Theorem for Hilbert Modules. Contemporary Mathematics 62, 429–435, AMS, Providence, 1987.zbMATHMathSciNetGoogle Scholar
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    J.A. Mingo, On the contractibility of the unitary group of the Hilbert space over a C*-algebra. Integral Eq. Operator Theory 5 (1982), 888–891.zbMATHMathSciNetCrossRefGoogle Scholar
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    G. Skandalis, Kasparov’s bivariant K-theory and applications. Exposition. Math. 9 (1991), no. 3, 193–250.zbMATHMathSciNetGoogle Scholar
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    K. Thomsen, On absorbing extensions. Proc. Amer.Math. Soc. 129 (2001), 1409–1417.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Vladimir Manuilov
    • 1
  • Klaus Thomsen
    • 2
  1. 1.Dept. of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of Mathematics Ny MunkegadeIMFAarhus CDenmark

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