Resonant superalgebras

Using a newly developed highly efficient computational method of generating 'resonating' algebraic structures, we achieve the supersymmetric extensions of algebras going beyond the Poincar\'e and Anti-de Sitter ones. Considered class of algebras include additional bosonic generators $Z_{ab}$ (Lorentz-like) and $U_a$ (translational-like) added to the standard Lorentz generator $J_{ab}$ and translation generator $P_{a}$. Our analysis includes cases up to two fermionic charges, $Q_{\alpha}$ and $Y_{\alpha}$. We reevaluated previously published results and obtained completely new algebras up to two of Lorentz-like, translation-like, and supercharge-like generators $(JP+Q)+(ZU+Y)=JPZU+QY$. In the last case, among 667 founded superalgebras 264 are suitable for supergravity construction.