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arXiv · 1601.00777

$*$-isomorphism of Leavitt path algebras over $\mathbb{Z}$

Toke Meier Carlsen
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Abstract

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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Toke Meier Carlsen. 2017-11-23. $*$-isomorphism of Leavitt path algebras over $\mathbb{Z}$. https://doi.org/10.1016/j.aim.2017.11.018

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