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User:Mct mht/Cuntz

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Classification

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The Cuntz algebras are pairwise non-isomorphic, i.e. and are non-isomorphic to nm. The K0 group of is Zn - 1, the abelian cyclic group of order n. Since K0 is a (functorial) invariant, and are non-isomorphic.

By extensions

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An extension of the compact operators by is a short exact sequence of C*-algebras

Descending to the Calkin algebra , extensions are in bijective correspondence with *-monomorphisms

Let π be the quotient map onto the Calkin algebra. Two extensions τ 1 and τ2 are said to be equivalent of

for some unitary U. They are weakly equivalent if

for some unitary u in .