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Resonant algebras and gravity. (English) Zbl 1364.81247

Summary: 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 a 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 the recently introduced \(\mathfrak{D}_m\). The additional new examples complete the resulting generalization of the bosonic enlargements for 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.

MSC:

81V17 Gravitational interaction in quantum theory
17B81 Applications of Lie (super)algebras to physics, etc.
20M14 Commutative semigroups
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
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