Branching systems and representations of Cohn–Leavitt path algebras of separated graphs

Abstract

For each separated graph (E,C) we construct a family of branching systems over a set X and show how each branching system induces a representation of the Cohn–Leavitt path algebra associated with (E,C) as homomorphisms over the module of functions in X. We also prove that the abelianized Cohn–Leavitt path algebra of a separated graph with no loops can be written as an amalgamated free product of abelianized Cohn–Leavitt algebras that can be faithfully represented via branching systems.