Leavitt Path Algebra over Kronecker Square of Quivers and Cross product algebra

In this paper, we initiate the study of Leavitt path algebra over Kronecker square of a quiver and show the similarities and contrast in the properties of Leavitt path algebra over a quiver and its Kronecker square. Furthermore, we discuss the connection of Leavitt path algebra over Kronecker square of a quiver with Hayashi's face algebra and the cross product algebra construction of the Leavitt path algebra over the original quiver.