Fusion rules for the orbifold vertex operator algebras $L_{\widehat{\frak{sl}_2}}(k,0)^{K}$

Abstract: For the Klein group $K$ and a positive integr $k$, irreducible modules of the orbifold vertex operator algebra $L_{\widehat{\mathfrak{sl}2}}(k,0)^{K}$ have been classified and constructed in \cite{JWa}. In this paper, we determine completely the fusion rules of $L{\widehat{\frak{sl}_2}}(k,0)^{K}$.