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I have a graded vector space $V$ and exterior algebra $\bigwedge V$.Suppose further that $V^0=V^1=0$.

I don't understand why $(\wedge V)^2=V^2,(\wedge V)^3=V^3$ and $(\wedge V)^4=P^2V^2$.

notation: $P^k V$ denotes the space of homogeneous degree-k polynomials with indeterminates living in $V$.

Thanks!

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