Resonant algebras and gravity

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.

17 pages, v3 (improved version prepared for publication in JPhysA)

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• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• An Analytic Method for $S$-Expansion involving Resonance and Reduction
• Infinite S-Expansion with Ideal Subtraction and Some Applications
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• Resonant algebras in Chern-Simons model of topological insulators
• On a Java library to perform S-expansions of Lie algebras
• A Java library to perform S-expansions of Lie algebras
• Resonant superalgebras for supergravity
• Boson-fermion algebraic mapping in second quantization
• $\mathcal{N}=2$ resonant superalgebra for supergravity