I have read something about generalized geometries from Gualtieri's thesis. At section 2.3 he discussed spinors. Here I have the question: Suppose that $ x+\xi \in V \oplus V^* $ we can define a bilinear form on $ V \oplus V^* $ by $(x+ \xi , y+ \nu)=1/2( \xi (y)+ \nu (x))$ Consider the Clifford algebra generated by $V$ and the bilinear form defined as above. Question: if ${e_i}$ is an orthonormal basis for $V$ and ${e^i}$ is its dual, what is the Clifford multiplication $e_i.e^j$?
Clifford multiplication in $V \oplus V^*$
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geometry
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0No, you didn't miss anything. $S$o because these two vectors are independent, so is their Cli$f$ford product. And because they are orthogonal, they anticommute. – 2012-07-12