Constructing Majorana Representations

Majorana theory was introduced by A. A. Ivanov as an axiomatic framework in which to study objects related to the Monster simple group and the Griess algebra. Since its inception, it has been used to construct a number of new and important subalgebras of the Griess algebra. The objects at the centre of the theory are known as Majorana algebras and can be studied either in their own right, or as Majorana representations of finite groups. In this paper, we present an algorithm to construct the Majorana representations of a given group. We also list a number of groups for which we have constructed Majorana representations, including some which give new examples of Majorana algebras. This work is inspired by that of A. Seress.