I spent a week in St Andrews working with Markus Pfeiffer on an ongoing project which we are working on writing and implementing an algorithm to construct 2-closed Majorana representations. Funding for this trip was provided by CoDiMa.

Majorana algebras are non-associate algebras used to study the Monster group and its subgroups. They can be studied either in their own right, or as Majorana representations of certain groups. Many examples of Majorana algebras have been constructed by hand but it has become clear that, in order to construct bigger and more interesting algebras, a more computational approach is needed.

In a celebrated paper in 2012, Akos Seress announced the existence of an algorithm to constuct 2-closed Majorana representations. Sadly Seress passed away in 2013 and the full details of his algorithm and his results were never published. Recovering his work has been an important aim of the theory ever since.

This was my second visit funded by CoDiMa to work on this project. After the first visit, we had implemented such an algorithm and had started to reproduce Seress’ results. However, constructing Majorana representations is very expensive both in terms of time and memory and so the algorithm requires a lot of optimisation, which was the focus of our work this time around.

The week was a sucess and we have now completely recovered Seress’ results and we are expecting to shortly be able to construct representations larger than those achieved by Seress.

Our work is available on GitHub.

Madeleine Whybrow