Kumjian-Pask algebras of finitely aligned higher-rank graphs

JOURNAL OF ALGEBRA

卷:482

Article

Clark, Lisa Orloff¹  Pangalela, Yosafat E. P.¹ 

[1] Univ Otago, Dept Math & Stat, POB 56, Dunedin 9054, New Zealand

关键词: Kumjian-Pask algebra;    Finitely aligned k-graph;    Steinberg algebra;   

DOI  :  10.1016/j.jalgebra.2017.03.038

来源: Elsevier

【 摘 要 】

We extend the definition of Kumjian-Pask algebras to include algebras associated to finitely aligned higher-rank graphs. We show that these Kumjian-Pask algebras are universally defined and have a graded uniqueness theorem. We also prove the Cuntz-Krieger uniqueness theorem; to do this, we use a groupoid approach. As a consequence of the graded uniqueness theorem, we show that every Kumjian-Pask algebra is isomorphic to the Steinberg algebra associated to its boundary path groupoid. We then use Steinberg algebra results to prove the Cuntz-Krieger uniqueness theorem and also to characterize simplicity and basic simplicity. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free