An isomorphism between the fusion algebras of $V_L^+$ and type $D^{(1)}$ level 2

Abstract

The fusion algebra of the vertex operator algebra $V_L^+$ for a rank 1 even lattice $L$ is explicitly shown to be isomorphic to the fusion algebra of the Kac-Moody algebra of type $D^{(1)}$ at level 2 in almost all cases.