Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions by simple $C^*$-algebras -- Quasidiagonal extensions   Let $A$ be an amenable separable \CA and $B$ be a non-unital but
$\sigma$-unital simple \CA with continuous scale. We show that two essential
extensions $\tau_1$ and $\tau_2$ of $A$ by $B$ are approximately unitarily
equivalent if and only if $$ [\tau_1]=[\tau_2] {\rm in} KL(A, M(B)/B). $$ If
$A$ is assumed to satisfy the Universal Coefficient Theorem, there is a
bijection from approximate unitary equivalence classes of the above mentioned
extensions to $KL(A, M(B)/B).$ Using $KL(A, M(B)/B),$ we compute exactly when
an essential extension is quasidiagonal. We show that quasidiagonal extensions
may not be approximately trivial. We also study the approximately trivial
extensions.

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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph