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arXiv · 2311.05694

A note on projections in \'etale groupoid algebras and diagonal preserving homomorphisms

Benjamin Steinberg
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Abstract

Carlsen (Adv.~Math, 2018) showed that any $\ast$-homomorphism between Leavitt path algebras over $\mathbb Z$ is automatically diagonal preserving and hence induces an isomorphism of boundary path groupoids. His result works over conjugation-closed subrings of $\mathbb C$ enjoying certain properties. In this paper, we characterize the rings considered by Carlsen as precisely those rings for which every $\ast$-homomorphism of algebras of Hausdorff ample groupoids is automatically diagonal preserving. Moreover, the more general groupoid result has a simpler proof.

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Benjamin Steinberg. 2023-11-09. A note on projections in \'etale groupoid algebras and diagonal preserving homomorphisms. https://arxiv.org/abs/2311.05694

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