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9 pages.-- PACS nrs.: 04.40.Nr, 11.15.-q, 02.40.Ma.-- MSC1991 codes: 53C30, 53C50, 53C80.-- Issue title: "Relativity and Gravitation".All of the homogeneous Lorentzian structures on the oscillator group equipped with a biinvariant Lorentzian metric, and then the associated reductive pairs, are obtained. Some of them are solutions of the Einstein-Yang-Mills equations.Partially supported by DGES (Spain) under Project PB95-0124, and by Xunta de Galiza, under Project XUGA 20703B98.Peer reviewe

Reductive decompositions and Einstein–Yang–Mills equations associated to the oscillator group