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

[摘要] 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. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Leavitt path algebras;Steinberg algebras