Superalgebras of (split-)division algebras and the split octonionic M-theory in (6,5)-signature

Physics NotePublished

Superalgebras of (split-)division algebras and the split octonionic $M$ -theory in $(6,5)$ -signature

Zhanna Kuznetsova

10/23/2006

Authors: Zhanna Kuznetsova
Type: Physics Note
Status: Published
Publication date: 23/10/2006
Description: 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 split-quaternions. Finally, we construct generalized supersymmetries admitting bosonic tensorial central charges in terms of (split-)division algebras. In particular we prove that split-octonions allow to introduce a split-octonionic $M$-algebra which extends to the $(6,5)$ signature the properties of the $11$-dimensional octonionic $M$-algebras (which only exist in the $(10,1)$ Minkowskian and $(2,9)$ signatures).
Year: 2006
Linked to a thesis: No
Linked to a grant: No