Leavitt path algebras of quantum quivers

Abstract

Adapting a recent work of Brannan et al. on extending graph \(C^*\)-algebras to quantum graphs, we introduce “Quantum Quivers” as an analogue of quivers where the edge and vertex set has been replaced by a \(C^*\)-algebra and the maps between the sets by \(*\)-homomorphisms. Additionally, we develop the theory around these structures and construct a notion of Leavitt path algebra over them and also compute the monoid of finitely generated projective modules over this class of algebras.