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Math Help - Anticommutativity involving odd part of clifford algebras.

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    Anticommutativity involving odd part of clifford algebras.

    I want to show that if w∈Cℓ1(V,Q) anticommutes with all v∈V, then w=0. I've been having a bit of trouble though.
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    Re: Anticommutativity involving odd part of clifford algebras.

    Quote Originally Posted by idontknowanything View Post
    I want to show that if w∈Cℓ1(V,Q) anticommutes with all v∈V, then w=0. I've been having a bit of trouble though.
    Hint: Recall that if \text{char}(k)\ne2, then there is a certain symmetric bilinear form \langle-,-\rangle in terms of Q such that uv+vu=2\langle u,v\rangle for all u,v\in V. Clearly then the result follows. If you aren't aware of this result, this at least tells you which v to plus in to anti commutativity to get that w=0 (namely, w)
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