On parafermion vertex algebras of $\frak{sl}(2)_{-3/2}$ and
$\frak{sl}(3)_{-3/2}$
On parafermion vertex algebras of $\frak{sl}(2)_{-3/2}$ and
$\frak{sl}(3)_{-3/2}$
We study parafermion vertex algebras $N_{-3/2}(\frak{sl}(2))$ and $N_{-3/2}(\frak{sl}(3))$. Using the isomorphism between $N_{-3/2}(\frak{sl}(3))$ and the logarithmic vertex algebra $\mathcal{W}^{0} (2)_{A_2} $ from [2], we show that these parafermion vertex algebras are infinite direct sums of irreducible modules for the Zamolodchikov algebra $\mathcal{W}(2,3)$ of central charge $c=-10$, and that $N_{-3/2}(\frak{sl}(3))$ is …