Leavitt Path Algebras of Quantum Quivers

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to Quantum graphs, we introduce “Quantum Quivers” as an analogue of quivers where the edge and vertex set has been replaced by a $C^{\ast }$-algebra and the maps between the sets by $\ast$-homomorphisms.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