Representations and the reduction theorem for ultragraph Leavitt path algebras

In this paper, we study representations of ultragraph Leavitt path algebras via branching systems and, using partial skew ring theory, prove the reduction theorem for these algebras. We apply to show that are semiprime and completely describe faithfulness arising from systems, in terms dynamics systems. Furthermore, permutative provide a sufficient criteria representation an algebra be equivalent system. class ultragraphs which every (satisfying mild condition) is has restriction