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arXiv · 2103.02712

A classification of ideals in Steinberg and Leavitt path algebras over arbitrary rings

Simon W. Rigby·Thibaud van den Hove
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Abstract

We give a one-to-one correspondence between ideals in the Steinberg algebra of a Hausdorff ample groupoid $G$, and certain families of ideals in the group algebras of isotropy groups in $G$. This generalises a known ideal correspondence theorem for Steinberg algebras of strongly effective groupoids. We use this to give a complete graph-theoretic description of the ideal lattice of Leavitt path algebras over arbitrary commutative rings, generalising the classification of ideals in Leavitt path algebras over fields.

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Simon W. Rigby, Thibaud van den Hove. 2021-03-03. A classification of ideals in Steinberg and Leavitt path algebras over arbitrary rings. https://arxiv.org/abs/2103.02712

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