Resonant enlargements of the Poincare/AdS (super)algebras from pattern-based analysis

Applying an efficient pattern-based computational method of generating the so-called ‘resonating’ algebraic structures results in a broad class of the new Lie (super)algebras. Those structures inherit the AdS base (anti)commutation pattern and can be treated as the enlargements of the Poincaré or Anti-de-Sitter (super)algebras. Obtained superalgebras are rooted in the semigroup expansion method and Maxwell and Soroka-Soroka algebras, spanned by the Lorentz generator $J_{ab}$, translations $P_a$ and additional Lorentz-like generator $Z_{ab}$. Considered configurations include cases up to two fermionic supercharges $Q_{\alpha }$ and offer interesting modifications to the gauge (super)gravity theories.