Participants
Joseph Liddell
An algebra is a linear space with a multiplication. Important examples include the real (or complex) matrices and the real valued functions on a space. Often algebras have additional structure. Hopf algebras provide a generalisation of the mathematical notion of symmetry. My project involved learning how to manipulate equations and solve them in different Hopf algebras. Overall, I managed to find all solutions to the generalised reflection equation (so-called Universal K-matrices) in the following three Hopf algebras: Sweedler’s Hopf-algebra, the group algebra of a finite group, and the quantum double of the group algebra. The latter two classes form infinite families of Hopf algebras, and I was able to give a classification of Universal K-matrices for these families. I then wrote a report containing the classification results and their proofs.
Funded by: Newcastle University Research Scholarship
Project Supervisor: Dr Stefan Kolb