Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primitive ideal space of Higher-rank graph $C^*$-algebras and
  decomposability   In this paper, we describe primitive ideal space of the $C^*$-algebra
$C^*(\Lambda)$ associated to any locally convex row-finite $k$-graph $\Lambda$.
To do this, we will apply the Farthing's desourcifying method on a recent
result of Carlsen, Kang, Shotwell, and Sims. We also characterize certain
maximal ideals of $C^*(\Lambda)$.
  Furthermore, we study the decomposability of $C^*(\Lambda)$. We apply the
description of primitive ideals to show that if $I$ is a direct summand of
$C^*(\Lambda)$, then it is gauge-invariant and isomorphic to a certain
$k$-graph $C^*$-algebra. So, we may characterize decomposable higher-rank
$C^*$-algebras by giving necessary and sufficient conditions for the underlying
$k$-graphs. Moreover, we determine all such $C^*$-algebras which can be
decomposed into a direct sum of finitely many indecomposable $C^*$-algebras.

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The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph