Cosmological constant, supersymmetry, nonassociativity, and Big Numbers

The nonassociative generalization of supersymmetry is considered. It is shown that the associator of four supersymmetry generators has the coefficient $\sim \hbar/ \ell_0^2$where$\ell_0$ is some characteristic length. Two cases are considered: (a) ${\mathrm{\ell }}_0^{-2}$ coincides with the cosmological constant; (b) ${\mathrm{\ell }}_0$ is the classical radius of electron. It is also shown that the scaled constant is of the order of ${10}^{-120}$ for the first case and ${10}^{-30}$ for the second case. The possible manifestation and smallness of nonassociativity is discussed.