Clifford Algebra
Note 2
Anti-automorphism
TANAKA Akio
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.
Duplicability Theory / Antiworld / Tokyo December 26, 2005
Also refer to the next.
Mirror Theory / Tokyo June 5, 2004
Mirror Language / Tokyo June 10, 2004
Guarantee of Language / Tokyo June 12, 2004
Actual Language and Imaginary Language / Tokyo September 23, 2004
Tokyo January 12, 2008
Sekinan Research Field of Language
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