Tuesday 6 January 2015

Clifford Algebra Note 2 Anti-automorphism / January 12, 2008

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 ( )
Ideal of T ( V )     Ithat is generated from all the elements of vw + wv + 2Q(v, w)     (vwV)
Clifford algebra     VQ ) = T ( ) / IQ
2
) Clifford module    E
Super module     E = E+  E-
C+(V)·
C-(V)·
3
Automorphism of V     v  v* = -v   ( vV )
4
Anti-automorphism of T ( )     (vw)* = w*v*   ( vwT ( ) )
5
Anti-automorphism of C ( ) : = 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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