Unitary spaces on Clifford algebras

Abstract

For the complex Clifford algebra Cl(p,q) of dimension n=p+q we define a Hermitian scalar product. This scalar product depends on the signature (p,q) of Clifford algebra. So, we arrive at unitary spaces on Clifford algebras. With the aid of Hermitian idempotents we suggest a new construction of, so called, normal matrix representations of Clifford algebra elements. These representations take into account the structure of unitary space on Clifford algebra.

39 pages

References in corpus (1)

• Dirac-type tensor equations with non-Abelian gauge symmetries on pseudo-Riemannian space

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• On Rank of Multivectors in Geometric Algebras
• Introducing Multidimensional Dirac-Hestenes Equation
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• Lorentz Invariance of the Multidimensional Dirac-Hestenes Equation