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

JOURNAL OF ALGEBRA

卷:588

Article

Rigby, Simon W.¹  van den Hove, Thibaud² 

[1] Univ Ghent, Dept Math Algebra & Geometry, Ghent, Belgium

[2] Univ Bonn, Math Inst, Bonn, Germany

关键词: Leavitt path algebras;    Steinberg algebras;   

DOI  :  10.1016/j.jalgebra.2021.08.021

来源: Elsevier

【 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.

【 授权许可】

Free