Quantum spheres as Leavitt path algebras: Quivers with Quantum Yang-Baxter equation, and Hecke condition

In this paper we study Leavitt path algebras over quivers with relations such as quantum Yang-Baxter equation, Hecke condition, and RTT conditions. This construction allows us to produce examples of Leavitt path algebras that contain quantum matrix algebra as subalgebra and obtain an algebraic analogue of the Hong-Szymański result. In particular, we show that the coordinate algebra over odd-dimensional Vaksman-Soibelman quantum sphere can be realized as the Zhang twist of a Leavitt path algebra over a quiver with such relations. Furthermore, we show that the quantum Yang-Baxter equation, and Hecke condition for our RTT construction can be generated intrinsically from the adjacency matrix of certain quivers.