Rigidity of Corona Algebras

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Date

2015-08-28

Authors

Ghasemi, Saeed

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Abstract

In this thesis we use techniques from set theory and model theory to study the isomorphisms between certain classes of C*-algebras. In particular we look at the isomorphisms between corona algebras of the form Mk(n)(C)/Mk(n)(C) for sequences of natural numbers {k(n):nN}. We will show that the question ``whether any isomorphism between these C*-algebras is trivial", is independent from the usual axioms of set theory (ZFC). We extend the classical Feferman-Vaught theorem to reduced products of metric structures. This implies that the reduced powers of elementarily equivalent structures are elementarily equivalent. We also use this to find examples of corona algebras of the form Mk(n)(C)/Mk(n)(C) which are non-trivially isomorphic under the Continuum Hypothesis. This gives the first example of genuinely non-commutative structures with this property. In chapter 6 we show that SAW-algebras are not isomorphic to ν-tensor products of two infinite dimensional C*-algebras, for any C*-norm ν. This answers a question of S. Wassermann who asked whether the Calkin algebra has this property.

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Mathematics, Theoretical mathematics

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