Leavitt path algebras of quantum quivers

Adapting a recent work of Brannan et al. on extending graph \(C^*\) $C^{\ast }$ -algebras to quantum graphs, we introduce “Quantum Quivers” as an analogue of quivers where the edge and vertex set has been replaced by a \(C^*\) $C^{\ast }$ -algebra and the maps between the sets by \(*\) $\ast$ -homomorphisms.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.