Maxwell extensions of kinematical algebras via semigroup expansions and their Chern–Simons gravity realizations.
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Date
2026
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Publisher
Universidad de Concepción
Abstract
In this thesis, we present a Maxwell extension of the kinematical Lie algebras by promoting the Bacry–Lévy-Leblond cube to a semigroup expansion framework. Within this approach, we show that both non- and ultra-relativistic Maxwell algebras admitting nondegenerate invariant bilinear forms can be systematically obtained from different parent algebras through a unified expansion scheme, leading to a Maxwellian kinematical cube. We further show that both the original Bacry–Lévy-Leblond cube and its Maxwellian extension belong to an infinite hierarchy of generalized kinematical algebras generated by higher-order semigroups. The expansion method naturally provides the corresponding invariant tensors, allowing for the systematic construction of three-dimensional Chern–Simons gravity theories.
Description
Tesis presentada para optar al grado de Magíster en Ciencias con mención en Física.
Keywords
Algebra, Gravity