IDEALS OF STEINBERG ALGEBRAS OF STRONGLY EFFECTIVE GROUPOIDS, WITH APPLICATIONS TO LEAVITT PATH ALGEBRAS

被引：9

作者：

Clark, Lisa Orloff ^{[1
,2
]}

Edie-Michell, Cain ^{[3
]}

Huef, Astrid An ^{[1
,2
]}

Sims, Aidan ^{[4
]}

机构：

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

[2] Victoria Univ Wellington, Sch Math & Stat, POB 600, Wellington 6140, New Zealand

[3] Australian Natl Univ, Inst Math Sci, Union Lane, Canberra, ACT 2601, Australia

[4] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 371卷 / 08期

基金：

澳大利亚研究理事会;

关键词：

Groupoid; Steinberg algebra; Leavitt path algebra; Kumjian-Pask algebra; ideal structure; KUMJIAN-PASK ALGEBRAS; SIMPLICITY; COEFFICIENTS;

D O I：

10.1090/tran/7460

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the ideal structure of Steinberg algebras over a commutative ring with identity. We focus on Hausdorff groupoids that are strongly effective in the sense that their reductions to closed subspaces of their unit spaces are all effective. For such a groupoid, we completely describe the ideal lattice of the associated Steinberg algebra over any commutative ring with identity. Our results are new even for the special case of Leavitt path algebras; so we describe explicitly what they say in this context, and give two concrete examples.

引用

页码：5461 / 5486

页数：26

共 33 条

[1] The Leavitt path algebra of a graph [J].

Abrams, G ;

Pino, GA .

JOURNAL OF ALGEBRA, 2005, 293 (02) :319-334

[2]

Abrams G., 2017, LECT NOTES MATH, V2191

[3] Leavitt path algebras: the first decade [J].

Abrams, Gene .

BULLETIN OF MATHEMATICAL SCIENCES, 2015, 5 (01) :59-120

[4] TWO-SIDED CHAIN CONDITIONS IN LEAVITT PATH ALGEBRAS OVER ARBITRARY GRAPHS [J].

Abrams, Gene ;

Bell, Jason P. ;

Colak, Pinar ;

Rangaswamy, Kulumani M. .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2012, 11 (03)

[5]

[Anonymous], 2005, CBMS Regional Conference Series in Mathematics, DOI DOI 10.1090/CBMS/103.453

[6] Nonstable K-theory for graph algebras [J].

Ara, P. ;

Moreno, M. A. ;

Pardo, E. .

ALGEBRAS AND REPRESENTATION THEORY, 2007, 10 (02) :157-178

[7] Leavitt path algebras with at most countably many irreducible representations [J].

Ara, Pere ;

Rangaswamy, Kulumani M. .

REVISTA MATEMATICA IBEROAMERICANA, 2015, 31 (04) :1263-1276

[8]

Bates T., 2000, NEW YORK J MATH, V6, P307

[9] Simplicity of algebras associated to ,tale groupoids [J].

Brown, Jonathan ;

Clark, Lisa Orloff ;

Farthing, Cynthia ;

Sims, Aidan .

SEMIGROUP FORUM, 2014, 88 (02) :433-452

[10] Irreducible representations of Leavitt path algebras [J].

Chen, Xiao-Wu .

FORUM MATHEMATICUM, 2015, 27 (01) :549-574

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