Clifford Algebra Periodicity

Clifford Algebra

Note 6

Periodicity

TANAKA Akio

n-dimensional Euclid space with canonical inner product     Rⁿ

Clifford algebra corresponded with Rⁿ     C (Rⁿ)

Complexification of C (Rⁿ)     C (Rⁿ) ⊗ C

Arbitrary integer     n > 0

C (Rⁿ⁺²) ⊗_R C ≃  C (Rⁿ⁺²) ⊗_R End ( C² )   

C (R²ⁿ) ⊗_R C  ≃  End ( C²ⁿ )

C (R²ⁿ⁺¹) ⊗_R C ≃ End ( C²ⁿ ) ⊕ End ( C²ⁿ )

[Note]

Periodicity in Clifford algebra may be corresponded with periodicity of meaning in word of natural language.

At early work of <Quantum Theory for Language>, especially refer to the next papers’ comments of meaning factors in ancient Chinese inscriptions†on bone and tortoiseshell <Jiaguwen>.

†On inscription < 亙geng>

On Time Property Inherent in Characters / 1 Generation of Characters / Hakuba March 28, 2003

†On inscription < 困 kun>

Prague Theory / Dedicated to KARCEVSKIJ, PRAGUE and CHINO / 9 Chinese character /kun/ / Tokyo October 2, 2004

Tokyo January 26, 2008

Sekinan Research Field of Language