Research talk: On the Classification of Generalized Cartan Matrices of Rank 3

Abstract

In this talk we describe very briefly how Gritsenko and Nikulin classified in \cite{3} the generalised Cartan matrices of rank 3, of elliptic type (so they have the generalised lattice Weyl vector), which are twisted to symmetric generalised Cartan matrices. We then introduce a conjecture on this classification and propose an algorithm for attacking it. The author would like to thank prof. V.V. Nikulin for giving him the opportunity to study this subject.