Note 2
Anti-automorphism
1
n-dimensional real vector space V
Inner product of V Q
Tensor algebra of V T ( V )
Ideal of T ( V ) IQ that is generated from all the elements of v⊗w + w⊗v + 2Q(v, w) (v, w∈V)
Clifford algebra C ( V, Q ) = T ( V ) / IQ
2
C ( V ) Clifford module E
Super module E = E+ ⊕ E-
C+(V)·
⊂
⊂
C-(V)·⊂
⊂
3
Automorphism of V v → v* = -v ( v∈V )
4
Anti-automorphism of T ( V ) (vw)* = w*v* ( v, w∈T ( V ) )
5
Anti-automorphism of C ( V ) : = a → a*
[Reference]
World and anti-world is considerable from Clifford algebra’s anti-automorphism.
Refer to the next.
Also refer to the next.
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