University of Sydney Algebra Seminar

Dilshan Wijesena

Friday 4 April, 12-1pm, in Carslaw 175

Moduli spaces for Leavitt path algebras

In this talk I will explain how the machinery of Vaughan Jones, originally developed for subfactor and conformal field theories, have been adapted to study representations of the LPAs. In particular, I will show how from a quiver representation one can obtain a representation of the LPA. Remarkably, this process preserves irreducible classes and yields an equivalence between certain subcategories. This will allow us to obtain moduli spaces for LPAs. We end by showing how many known irreducible representations of LPAs arise from finite-dimensional quiver representations using our techniques. Minimal knowledge is required and all are welcomed! This is a joint work with Arnaud Brothier.