Student Profile: Courtney Darville

Courtney Darville

The University of Sydney

Biography

Courtney Darville is a third-year mathematics student at the University of Sydney. She is about to pursue her honours degree in pure mathematics. Courtney’s interests so far have been in the fields of group theory and differential geometry. Her interests outside mathematics include rock climbing and cycling.

Characterising unitaries in Leavitt algebras

The embedding problem in the field of Leavitt path algebras is an open problem which concerns the embedding of tensor products in the Leavitt algebra of module type (1,2). Recent results show that there is a negative answer to the embedding problem when the coefficient ring is the integers.

In this project, we aim to extend the class of coefficient rings for which we have an answer to the embedding problem. Our key technique will be to characterise unitary elements in the Leavitt algebra module type (1,2). We aim to do this when the coefficient ring is a finite field, and when it has an essentially unique partition of the unit.

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