= Clifford algebra
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For a <vector space> $V$ over a <field> of <characteristic> different from two and a <quadratic form> $Q$, its <Clifford algebra> is the <quotient> of the <tensor algebra> by the relations $v^2=Q(v)1$. Writing $B(u,v)=(Q(u+v)-Q(u)-Q(v))/2$ gives $uv+vu=2B(u,v)1$.
For a real two-dimensional positive-definite form and an <orthonormal basis> $e_1,e_2$, the generators satisfy $e_1^2=e_2^2=1$ and $e_1e_2=-e_2e_1$. The algebra has <basis> $1,e_1,e_2,e_1e_2$. Its <Clifford modules> provide spinor spaces, while products of suitable unit vectors represent rotations. The sign convention on $Q$ must be stated, especially when comparing geometric and physical conventions.
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