ORBIT EQUIVALENCE OF GRAPHS AND ISOMORPHISM OF GRAPH GROUPOIDS

被引：8

作者：

Carlsen, Toke Meier ^{[1
]}

Winger, Marius Lie ^{[2
]}

机构：

[1] Univ Faroe Isl, Dept Sci & Technol, Noatun 3, FO-100 Torshavn, Denmark

[2] Norwegian Univ Sci & Technol, Fac Teacher & Interpreter Educ, Dept Teacher Educ & BA Arch & Collect Managem 1 7, Postboks 8900, N-7491 Trondheim, Norway

来源：

MATHEMATICA SCANDINAVICA | 2018年 / 123卷 / 02期

关键词：

ALGEBRAS;

D O I：

10.7146/math.scand.a-105087

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the groupoids of two directed graphs are isomorphic if and only if the two graphs are orbit equivalent by an orbit equivalence that preserves isolated eventually periodic points. We also give a complete description of the (topological) isolated points of the boundary path space of a graph. As a result, we are able to show that the groupoids of two directed graphs with finitely many vertices and no sinks are isomorphic if and only if the two graphs are orbit equivalent, and that the groupoids of the stabilisations of two such graphs are isomorphic if and only if the stabilisations of the graphs are orbit equivalent.

引用

页码：239 / 248

页数：10

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