# Degree part of exterior algebra

by sasho98   Last Updated July 12, 2019 07:20 AM

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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