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Advances in Applied Clifford Algebras

, Volume 18, Issue 2, pp 197–236 | Cite as

The Graded Structure of Nondegenerate Meson Algebras

  • Jacques HelmstetterEmail author
  • Artibano Micali
Article

Abstract.

Meson algebras are involved in the wave equation of meson particles in the same way as Clifford algebras are involved in the Dirac wave equation of electrons. Here we improve and generalize the information already obtained about their structure and their representations, when the symmetric bilinear form under consideration is nondegenerate. We emphasize their parity grading. We calculate the center of these meson algebras, and the center of their even subalgebra. Finally we show that every nondegenerate meson algebra over a field contains a group isomorphic to the group of automorphisms of the symmetric bilinear form.

Mathematics Subject Classification (2000).

15A66 15A78 16S10 16W50 81R05 81R20 

Keywords.

Clifford algebras other algebras built from modules algebras determined by universal properties graded algebras and modules algebras motivated by Physics and their representations wave equations 

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Copyright information

© Birkhauser 2008

Authors and Affiliations

  1. 1.Institut Fourier (Mathématiques)Université Grenoble ISaint-Martin d’HèresFrance
  2. 2.Département des Sciences MathématiquesUniversité Montpellier IIMontpellier Cedex 5France

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