21 Involutions Acting on the Moonshine Module Original Research Article

We constructed the set of 21 involution automorphisms of the Moonshine module corresponding to 9 points and 12 lines of the affine plane of order 3 and satisfying the Coxeter relations of the incident matrix by using deep hole isotropic elements of Lorentzian lattice of dimension 26. Furthermore, all symmetries of this plane are automorphisms of the Moonshine module.