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

TL;DR

This paper introduces a pattern-based computational method to generate new Lie (super)algebras that extend Poincaré and AdS algebras, with potential applications in gauge supergravity theories.

Contribution

It presents a novel pattern-based approach for deriving a broad class of resonating algebraic structures that extend known superalgebras, rooted in semigroup expansion techniques.

Findings

Generated new Lie (super)algebras with AdS-like structures

Included cases with up to two fermionic supercharges

Proposed modifications to gauge (super)gravity theories

Abstract

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 Poincar\'{e} 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.