2006/10/10 by Zhanna Kuznetsova, Kuznetsova, Zhanna, Francesco Toppan +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.hep-th/0610122
16 pages
arxiv created 2006/10/10 · arxiv updated 2009/12/01
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).