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Tuesday, 18 March 2025

Clifford Algebra Note 2 Anti-automorphism

 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

www.sekinan.org

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