This package is built to work with so-called axial algebras: a class of nonassociative algebras carrying representations of transposition groups. A particular application is to Majorana theory and hence the Monster.

It requires the Transposition Groups package, available at https://github.com/felixrehren/trgps.

To set up the package, install the folder axials in your GAP packages directory. For me, that's in ~/.gap/pkg/. This is everything.

In GAP, load the package with the command LoadPackage("axials");. Here are some sample commands.

Vir43 := VirasoroFusion(4,3);
Fields( Vir43 );
Fuse( V43 )( 1/4,1/4 );

GetAxialRep( Vir43 );
R := GetAxialRep( Vir43, Dih(4) )[2];
FindForm( R );
CentralCharge( Axes(R)[1] );
Idempotents( Alg(R) );

T := TranspositionGroup( Sym(3), [(1,2)] );
R := FindUniversalAxialRep( T, Vir43 );
a := Axes(R)[1];
Eigenspaces(a);
Rs := Explode( R );
List( Rs, RecogniseShape );

TT := GroupToTrgps( Sym(4), 6 );
SS := Shapes( TT[1], MajoranaSakuma );
RR := List( SS, S -> FindAxialRep( S, Vir43 ) );