(2018) Shumba, Tendai M. Mudziiri.; Rodrigues, Bernardo Gabriel.; Shpectorov, Sergey.
Motivated by the construction of the Monster sporadic simple group as a
group of automorphisms of an algebra and the recent development of ax- ial algebras as a
generalization of Majorana representations, we construct axial algebras for the sporadic simple
groups HS and Suz in different ways analogous to the Norton algebra construction. We study how
these algebras decompose as direct sums of the adjoint action of an axis. Fusion rules, that is the
rules with which eigenvectors from various eigenspaces of the adjoint action multiply, are found.
This places these groups in a general framework of groups acting on algebras hence giving a common
theme for their origin.
