Note 6
Periodicity
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>
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