Orthonormal Basis Sets in Clifford Algebras

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

A chapter in Clifford Algebras with Numeric and Symbolic Computations, 1996, pp 269-284 from Springer

Abstract: 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.

Keywords: Isomorphisms; automorphisms; representations; classification of real Clifford algebras (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-1-4615-8157-4_18

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