On Steinberg algebras of Hausdorff ample groupoids over commutative semirings

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Tran Giang Nam¹  Zumbraegel, Jens² 

[1] VAST, Inst Math, 18 Hoang Quoc Viet, Hanoi, Vietnam

[2] Univ Passau, Fac Comp Sci & Math, Passau, Germany

关键词: Etale groupoids;    Ample groupoids;    Congruence-simple semirings;    Steinberg algebras;    Leavitt path algebras;   

DOI  :  10.1016/j.jpaa.2020.106548

来源: Elsevier

【 摘 要 】

We investigate the algebra of a Hausdorff ample groupoid, introduced by Steinberg, over a commutative semiring S. In particular, we obtain a complete characterization of congruence-simpleness for such Steinberg algebras, extending the well-known characterizations when S is a field or a commutative ring. We also provide a criterion for the Steinberg algebra A(S)(G(E)) of the graph groupoid G(E) associated to an arbitrary graph E to be congruence-simple. Motivated by a result of Clark and Sims, we show that the natural homomorphism from the Leavitt path algebra L-B(E) to the Steinberg algebra A(B)(G(E)), where B is the Boolean semifield, is an isomorphism if and only if E is row-finite. Moreover, we establish the Reduction Theorem and Uniqueness Theorems for Leavitt path algebras of row-finite graphs over the Boolean semifield B. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free