Contractions of the Lie
algebras d = u(2), f = u(1
,1) to the oscillator Lie algebra l are realized via the adjoint action of SU(2,2) when d, l, f are viewed as subalgebras of su(2,2).
Here D, L, F are the
corresponding (four-dimensional) real Lie groups endowed with bi-invariant
metrics of Lorentzian signature. Similar contractions of (seven-dimensional)
isometry Lie algebras iso(D), iso(F) to iso(L) are determined.
The group SU(2,2) acts on each of the D, L, F by conformal transformation which is a core feature of the DLF-theory. Also, d and f are contracted to T, S-abelian subalgebras, generating
parallel translations, T, and proper
conformal transformations, S (from
the decomposition of su(2,2) as
a graded algebra T + Ω + S, where Ω is the extended Lorentz Lie
algebra of dimension 7).
Cite this paper
A. Levichev and O. Sviderskiy, "Contractions of Certain Lie Algebras in the Context of the DLF-Theory," Advances in Pure Mathematics
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