Vladimir Manuilov
Extensions of Hilbert C*-modules: classification in simple cases.
Tue, 03/20/2012 - 15:01 — SomNambulAuthors: Vladimir Manuilov, Jingming Zhu
Subjects: Operator Algebras
AbstractTheory of extensions of Hilbert C*-modules was developed by D. Bakic and B.
Guljas. An easy observation shows that in the case, when the underlying
C*-algebra extension is commutative and the Hilbert C*-modules are projective
of finite type, the algebraic properties of the corresponding Busby invariant
allow to identify extensions with isometric maps of the corresponding vector
bundles. When the Hilbert C*-modules are free of rank one, we evaluate the set
of extensions in topological terms.Shape theory and extensions of C*-algebras.
Tue, 07/13/2010 - 15:01 — SomNambulAuthors: Klaus Thomsen, Vladimir Manuilov
Subjects: Operator Algebras
AbstractLet $A$, $A'$ be separable $C^*$-algebras, $B$ a stable $\sigma$-unital
$C^*$-algebra. Our main result is the construction of the pairing
$[[A',A]]\times\operatorname{Ext}^{-1/2}(A,B)\to\operatorname{Ext}^{-1/2}(A',B)$,
where $[[A',A]]$ denotes the set of homotopy classes of asymptotic
homomorphisms from $A'$ to $A$ and $\operatorname{Ext}^{-1/2}(A,B)$ is the
group of semi-invertible extensions of $A$ by $B$. Assume that all extensions
of $A$ by $B$ are semi-invertible.
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