Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposable Leavitt path algebras for arbitrary graphs   For any field $K$ and for a completely arbitrary graph $E$, we characterize
the Leavitt path algebras $L_K(E)$ that are indecomposable (as a direct sum of
two-sided ideals) in terms of the underlying graph. When the algebra
decomposes, it actually does so as a direct sum of Leavitt path algebras for
some suitable graphs. Under certain finiteness conditions, a unique
indecomposable decomposition exists.

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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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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: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: q-bio