Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $*$-isomorphism of Leavitt path algebras over $\mathbb{Z}$   We characterise when the Leavitt path algebras over $\mathbb{Z}$ of two
arbitrary countable directed graphs are $*$-isomorphic by showing that two
Leavitt path algebras over $\mathbb{Z}$ are $*$-isomorphic if and only if the
corresponding graph groupoids are isomorphic (if and only if there is a
diagonal preserving isomorphism between the corresponding graph
$C^*$-algebras). We also prove that any $*$-homomorphism between two Leavitt
path algebras over $\mathbb{Z}$ maps the diagonal to the diagonal. Both results
hold for slight more general subrings of $\mathbb{C}$ than just $\mathbb{Z}$.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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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: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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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: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom