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 ( V )

Ideal of T ( V )     I_Q 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 ) / I_Q

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

www.sekinan.org