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Orthonormal Basis Sets in Clifford Algebras

In: Clifford Algebras with Numeric and Symbolic Computations

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  • G. Bergdolt

    (C.N.R.S, Centre de Recherches Nucleaires)

Abstract

Orthonormal basis sets define isomorphisms and automorphisms in Clifford algebras. Orthonormal basis sets (ONB) are defined as sets of multivectors satisfying scalar product relations. A FORTRAN program determining ONBs is described. It is shown that any simple Clifford algebra is isomorphic to the tensor product of a Clifford algebra Cℓ m,m and a Clifford algebra isomorphic to ℝ, ℂ or ℍ. From the construction of matrix algebras isomorphic to Cℓ m,m given by the second FORTRAN program, matrix algebras with entries in ℝ, ℂ or ℍ can be used to construct isomorphisms to all simple Clifford algebras.

Suggested Citation

  • G. Bergdolt, 1996. "Orthonormal Basis Sets in Clifford Algebras," Springer Books, in: Rafał Abłamowicz & Josep M. Parra & Pertti Lounesto (ed.), Clifford Algebras with Numeric and Symbolic Computations, pages 269-284, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-8157-4_18
    DOI: 10.1007/978-1-4615-8157-4_18
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