A note on $2$-plectic homogeneous manifolds

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In this note we study the existence of $2$-plectic structures on homogenous spaces. In particular we show that $S^{5}=\frac{SU(3)}{SU(2)}$, $\frac{SU(3)}{S^{1}}$, $\frac{SU(3)}{T^{2}}$ and $\frac{SO(4)}{S^{1}}$ admit a $2$-plectic structure. Furthermore, If $G$ is a Lie group with Lie algebra $\mathfrak{g}$ and $R$ is a closed Lie subgroup of $G$ corresponding to the nilradical of $\mathfrak{g}$, then $\frac{G}{R}$ is a $2$-plectic manifold.