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

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