Stability of semisimple superalgebras

Deformation equations for Lie superalgebras are constructed. It is shown that their solutions are elements of the corresponding cohomology groups of the superalgebra. It is shown that the cohomology groups $H^1(L, L)$ and $H^2(L, L)$ are trivial for semisimple superalgebras $L$ with nondegenerate Killing form, which means that they have weak stability. This result makes it possible to analyze the deformation of the bispinor extension of the Poincar6 algebra and prove the algebraic stability of this model.