Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The centre-quotient property and weak centrality for $C^*$-algebras   We give a number of equivalent conditions (including weak centrality) for a
general $C^*$-algebra to have the centre-quotient property. We show that every
$C^*$-algebra $A$ has a largest weakly central ideal $J_{wc}(A)$. For an ideal
$I$ of a unital $C^*$-algebra $A$, we find a necessary and sufficient condition
for a central element of $A/I$ to lift to a central element of $A$. This leads
to a characterisation of the set $V_A$ of elements of an arbitrary
$C^*$-algebra $A$ which prevent $A$ from having the centre-quotient property.
The complement $\mathrm{CQ}(A):= A \setminus V_A$ always contains
$Z(A)+J_{wc}(A)$ (where $Z(A)$ is the centre of $A$), with equality if and only
if $A/J_{wc}(A)$ is abelian. Otherwise, $\mathrm{CQ}(A)$ fails spectacularly to
be a $C^*$-subalgebra of $A$.

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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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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: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph