On the Triality of the Hamming Code Vertex Operator Algebra

We study a set of certain automorphisms of the Hamming code vertex operator algebra MH8, which permute the three sets of conformal vectors. We call this set the triality of HH8. We construct an embedding MH8 to the VOA VD4 associated to the lattice of type D4, and we establish that the triality of MH8 is obtained by restricting the automorphisms of VD4 that correspond to the classical triality of D4.