Representations of relative Cohn path algebras

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Gil Canto, Cristobal¹  Goncalves, Daniel² 

[1] Univ Malaga, Dept Algebra Geometria & Topol, E-29071 Malaga, Spain

[2] Univ Fed Santa Catarina, Departmento Matemat, BR-88040900 Florianopolis, SC, Brazil

关键词: Relative Cohn path algebras;    Uniqueness theorems;    Branching systems;    Faithful representations;    Partial skew group rings;    Reduction theorem;   

DOI  :  10.1016/j.jpaa.2020.106310

来源: Elsevier

【 摘 要 】

We study relative Cohn path algebras, also known as Leavitt-Cohn path algebras, and we realize them as partial skew group rings. To do this we prove uniqueness theorems for relative Cohn path algebras. Furthermore, given any graph E we define E-relative branching systems and prove how they induce representations of the associated relative Cohn path algebra. We give necessary and sufficient conditions for faithfulness of the representations associated to E-relative branching systems. This improves previous results known to Leavitt path algebras of row-finite graphs with no sinks. To prove this last result we show first a version, for relative Cohn-path algebras, of the reduction theorem for Leavitt path algebras. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free