Order Ideal Relations and Structural Properties of Leavitt Path Algebras

This project aims to explore connections between the graded isomorphisms of Leavitt algebras, the order units of their corresponding graded graph monoids and the (graded) IBN concepts. By proving an Order Unit equivalence criteria in the graded graph monoid that I identified over the summer of 2019-20, I will approach a conjecture concerning the criteria for graded isomorphism between the Leavitt path algebra of an arbitrary graph E and the graph with one vertex and n loops, an important graph in the area of Leavitt path algebras. The hope is that this may provide insight into the graded version of the algebraic Kirchberg-Phillips question that is suggested to be the most compelling open question in Leavitt path algebras.

Anthony Warwick

Western Sydney University

Anthony Warwick is currently undertaking a Bachelor of Mathematical Sciences at Western Sydney University. As a mature-age student and enthusiastic chin stroker, Anthony spent his twenties performing and composing music where he explored abstract ideas through modular synthesis directing him head first into mathematics. This obsession with general solutions, interaction and connectivity has led him to focus on Leavitt path algebras. Having already undertaken a research scholarship on Leavitt path algebras in 2019, in coming years Anthony hopes to complete an honours in Pure Mathematics followed by a PhD in a similar area.

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