Octonionic M-theory and D=11 generalized conformal and superconformal algebras

Following [Phys. Lett. B 539 (2002) 266] we further apply the octonionic structure to supersymmetric D=11 M-theory. We consider the octonionic 2n+1×2n+1 Dirac matrices describing the sequence of Clifford algebras with signatures (9+n,n) (n=0,1,2,…) and derive the identities following from the octonionic multiplication table. The case n=1 (4×4 octonion-valued matrices) is used for the description of the D=11 octonionic M-superalgebra with 52 real bosonic charges; the n=2 case (8×8 octonion-valued matrices) for the D=11 conformal M-algebra with 232 real bosonic charges. The octonionic structure is described explicitly for n=1 by the relations between the 528 Abelian O(10,1) tensorial charges Zμ, Zμν, Zμ…μ5 of the M-superalgebra. For n=2 we obtain 2080 real non-Abelian bosonic tensorial charges Zμν, Zμ1μ2μ3, Zμ1…μ6 which, suitably constrained describe the generalized D=11 octonionic conformal algebra. Further, we consider the supersymmetric extension of this octonionic conformal algebra which can be described as D=11 octonionic superconformal algebra with a total number of 64 real fermionic and 239 real bosonic generators.