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#### Prime ideals in quantum algebras

(The University of Edinburgh, 2009-01)

The central objects of study in this thesis are quantized coordinate algebras.
These algebras originated in the 1980s in the work of Drinfeld and Jumbo and are
noncommutative analogues of coordinate rings of algebraic ...

#### On the complexity of matrix multiplication

(The University of Edinburgh, 2010)

The evaluation of the product of two matrices can be very computationally expensive.
The multiplication of two n×n matrices, using the “default” algorithm can take O(n3)
field operations in the underlying field k. It is ...

#### Representations of rational Cherednik algebras: Koszulness and localisation

(The University of Edinburgh, 2014-07-01)

An algebra is a typical object of study in pure mathematics. Take a collection of numbers (for
example, all whole numbers or all decimal numbers). Inside, you can add and multiply, but
with respect to these operations ...

#### PBW deformations and quiver GIT for noncommutative resolutions

(The University of Edinburgh, 2015-07-01)

In this thesis we first investigate PBW deformations of Koszul, Calabi-Yau algebras, and we then
study moduli spaces of representations of algebras defined by tilting bundles. These classes of
algebras are generalisations ...