Kumjian-Pask algebras of finitely aligned higher-rank graphs

被引：18

作者：

Clark, Lisa Orloff ^{[1
]}

Pangalela, Yosafat E. P. ^{[1
]}

机构：

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

来源：

JOURNAL OF ALGEBRA | 2017年 / 482卷

关键词：

Kumjian-Pask algebra; Finitely aligned k-graph; Steinberg algebra; C-ASTERISK-ALGEBRAS; LEAVITT PATH ALGEBRAS; CUNTZ-KRIEGER ALGEBRAS; UNIQUENESS THEOREMS; STEINBERG ALGEBRAS; INVERSE SEMIGROUP; GROUPOID APPROACH; SIMPLICITY;

D O I：

10.1016/j.jalgebra.2017.03.038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：364 / 397

页数：34