Let $V = \mathbb H^n$ be a (right) $\mathbb H$-module with "scalar" multiplication defined by $$(v_1,\dots,v_n) \cdot \alpha = (v_1 \alpha, \dots, v_n \alpha)$$ for $\alpha$ and $v_i$ in $ \mathbb H$.
Because $V$ is a real vector space, we can talk about the exterior product $\Lambda^2 (V)$.
My question: is there any (right) $\mathbb H$-module strucutre on the exterior product $\Lambda^2 (V)$ which is related (or maybe not) to the module structure on $V$ defined above?