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Advances in Applied Clifford Algebras

, Volume 18, Issue 2, pp 237–254 | Cite as

Unitary Spaces on Clifford Algebras

  • N. G. MarchukEmail author
  • D. S. Shirokov
Article

Abstract.

For the complex Clifford algebra Open image in new window (p, q) of dimension npq 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.

Mathematics Subject Classification (2000).

Primary 15A66 

Keywords.

Clifford algebra unitary space commutator Hermitian idempotents matrix representations 

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Copyright information

© Birkhauser 2008

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia

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