SUBSETS OF VERTICES GIVE MORITA EQUIVALENCES OF LEAVITT PATH ALGEBRAS

被引：1

作者：

Clark, Lisa Orloff ^{[1
]}

Huef, Astrid An ^{[1
]}

Luiten-Apirana, Pareoranga ^{[1
]}

机构：

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

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2017年 / 96卷 / 02期

关键词：

directed graph; Leavitt path algebra; Morita context; Morita equivalence; graph algebra; C-ASTERISK-ALGEBRAS; GRAPH ALGEBRAS; ARBITRARY GRAPHS;

D O I：

10.1017/S0004972717000247

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that every subset of vertices of a directed graph E gives a Morita equivalence between a subalgebra and an ideal of the associated Leavitt path algebra. We use this observation to prove an algebraic version of a theorem of Crisp and Gow: certain subgraphs of E can be contracted to a new graph G such that the Leavitt path algebras of E and G are Morita equivalent. We provide examples to illustrate how desingularising a graph, and in- or out-delaying of a graph, all fit into this setting.

引用

页码：212 / 222

页数：11

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