A. V. Levichev, “Certain Symmetric General Relativistic Space-Times as the Solutions to the Einstein-Yang-Mills Equations,”, Proceedings Group Theoretical Methods in Physics (III International Seminar), Yurmala, 1985, pp. 145-150. (in Russian)

has been cited by the following article:

• TITLE: Contractions of Certain Lie Algebras in the Context of the DLF-Theory

  AUTHORS: Alexander Levichev, Oleg Sviderskiy

  KEYWORDS: Lie Algebras with Invariant Lorentzian Forms; Lorentzian Symmetric Spaces; Contractions of Lie Algebras; Conformal Lie Algebra; Segal’s Chronometric Theory; DLF-Theory

  JOURNAL NAME: Advances in Pure Mathematics, Vol.4 No.1, January 8, 2014

  ABSTRACT: 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).