Characterization of semidirect sum Lie algebras

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Abstract
Semidirect sum Lie algebras 𝒜■𝒳 may be characterized by the type of the representation the invariant subalgebra 𝒳 provides for the Lie algebra 𝒜. The method is of particular interest when the invariant subalgebra 𝒳 is infinite dimensional and allows one to compare such algebras provided the representations of the algebra 𝒜 are known. In this way two infinite semidirect sum Lie algebras of the Lorentz algebra, namely the relativistic internal time algebra and the Bondi–Metzner–Sachs algebra, are characterized. Furthermore some minor errors of the commutation relations of the Bondi–Metzner–Sachs algebra have been corrected.

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