I have a graded vector space $V$ such that $V=V^2\bigoplus V^3$, i.e $V^k=0\quad \forall k\neq2,3.$
Now I can't understand what is $\bigwedge V^{\leq 2}$.
Is it $\bigwedge V^{\leq 2}=\bigwedge^0 V^{\leq 2}\bigoplus \bigwedge^1 V^{\leq 2}\bigoplus...$ with $V^{\leq 2}=V^2$?
Also what is $(\bigwedge V^{\leq 2})^2$?
Thanks!