Resonant algebras and gravity

TL;DR

This paper explores the $S$-expansion method for Lie algebras, revealing new classes of algebras that modify gauge gravity theories and providing tools for constructing related gravity actions.

Contribution

It generalizes the $S$-expansion framework by including zero elements and identity mappings, leading to new Maxwell algebra classes and broadening algebraic structures for gravity models.

Findings

All Maxwell algebras of types $rak{B}_m$, $rak{C}_m$, and $rak{D}_m$ identified.

New algebraic structures with extended Lorentz and translational generators constructed.

Framework for building gravity actions from these expanded algebras established.

Abstract

The $S$-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition and associating the Lorentz generator with the semigroup identity element leads to the wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type $\mathfrak{B}_m$, $\mathfrak{C}_m$, and recently introduced $\mathfrak{D}_m$. The additional new examples complete resulting generalization of the bosonic enlargements to an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.