Division algebra representations of SO(4, 2)
Abstract
Representations of SO(4, 2) are constructed using 4×4 and 2×2 matrices with elements in ℍ' ⊗ ℂ and the known isomorphism between the conformal group and SO(4, 2) is written explicitly in terms of the 4×4 representation. The Clifford algebra structure of SO(4, 2) is briefly discussed in this language, as is its relationship to other groups of physical interest.
 Publication:

Modern Physics Letters A
 Pub Date:
 August 2014
 DOI:
 10.1142/S0217732314501284
 arXiv:
 arXiv:1312.7391
 Bibcode:
 2014MPLA...2950128K
 Keywords:

 Division algebras;
 magic squares;
 orthogonal groups;
 Clifford algebras;
 11.10.Kk;
 11.30.Cp;
 11.30.Ly;
 Field theories in dimensions other than four;
 Lorentz and Poincare invariance;
 Other internal and higher symmetries;
 Mathematics  Rings and Algebras;
 22E46 (primary);
 22E70;
 81R05 (secondary)
 EPrint:
 13 pages