Superalgebras of (split)division algebras and the split octonionic Mtheory in (6,5)signature
Abstract
The connection of (split)division algebras with Clifford algebras and supersymmetry is investigated. At first we introduce the class of superalgebras constructed from any given (split)division algebra. We further specify which real Clifford algebras and real fundamental spinors can be reexpressed in terms of splitquaternions. Finally, we construct generalized supersymmetries admitting bosonic tensorial central charges in terms of (split)division algebras. In particular we prove that splitoctonions allow to introduce a splitoctonionic Malgebra which extends to the (6,5) signature the properties of the 11dimensional octonionic Malgebras (which only exist in the (10,1) Minkowskian and (2,9) signatures).
 Publication:

arXiv eprints
 Pub Date:
 October 2006
 arXiv:
 arXiv:hepth/0610122
 Bibcode:
 2006hep.th...10122K
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 16 pages