Realization, Classification, and Extension of Certain Physically Important Groups and Algebras

Oct, 1979
35 pages
Published in:
  • J.Math.Phys. 22 (1981) 226
Report number:
  • Print-79-0895 (MASS.U.,BOSTON)

Citations per year

19811991200120112019012345
Abstract: (AIP)
An associative algebra of differential forms with division has been constructed. The algebra of forms in each different space provides a practical realization of the universal Clifford algebra of that space. A classification of all such algebras is given in terms of two distinct types of algebrasN k and S k . The former include the dihedral, quaternion, and Majorana algebras; the latter include the complex, spinor, and Diracalgebras. The associative product expresses Hodge duality as multiplication by a basis element. This makes possible the realization of higher order algebras in a calculationally useful algebraic setting. The fact that the associative algebras, as well as the enveloped Lie algebras, are precisely those arising in physics suggests that this formalism may be a convenient setting for the formulation of basic physical laws.
  • GROUP THEORY: DUALITY
  • ALGEBRA: CLIFFORD
  • ALGEBRA: QUATERNION
  • ALGEBRA: MAJORANA
  • ALGEBRA: SPINOR
  • SPINOR: ALGEBRA
  • ALGEBRA: DIRAC
  • ALGEBRA: LIE
  • ALGEBRA: JORDAN