Representations of relative Cohn path algebras
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.03077
- arXiv:
- arXiv:1806.03077
- Bibcode:
- 2018arXiv180603077G
- Keywords:
-
- Mathematics - Rings and Algebras;
- Mathematics - Operator Algebras;
- 16S99;
- 16G99
- E-Print:
- 20 pages