Nikolaus Conference 2018

The simple Lie algebras are classified over all algebraically closed fields in characteristic \(0\) and in characteristic \(p > 3\). The small characteristics \(2\) and \(3\) are still open cases. The available evidence suggests that the classification in small characteristic is very different from that in characteristic \(p > 3\). This talk shows how computational methods can be used to search for new simple Lie algebras over \(GF(2)\). The computational methods exhibited in this talk have been used to find some new simple Lie algebras in dimensions up to \(20\). This project is still ongoing and there is the aim to extend this search to larger dimensions. The talk will also discuss the main problems that need to be addressed for this purpose. This talk is based on joint work with Bettina Eick (TU Braunschweig).