Leavitt path algebras and graphs

Abstract

A graph is a collection of vertices and edges that connect to each other. For any directed graph E and any field K, the Leavitt path algebra of E, denoted LK(E) can be constructed. Ve define grading on ring, module, and matrix, and we show that LK(E) could be naturally Z-graded algebra. Ve characterize the structure of the Leavitt path algebras associated to finite acyclic graphs and Cn-comets. Then, we characterize these types of graphs considering the Z-grading of the algebra. Ve also characterize Leavitt path algebras which are strongly graded. To complete the characterisation of LK(E), we study the graph monoids and the tal- ented monoids associated to a graph. Ve finish the project by a complete characterization of the structure of Leavitt path algebras, which is the crossed product in terms of the geometry of the graph.

Date of Award	2024
Original language	English
Awarding Institution	Western Sydney University
Supervisor	Roozbeh Hazrat (Supervisor) & James East (Supervisor)