We classify four-dimensional connected simply-connected Lorentzian symmetric spaces M with connected nontrivial isotropy group furnishing solutions of the Einstein–Yang–Mills equations. Those solutions are built with respect to some invariant metric connection \(\Lambda \) in the bundle of orthonormal frames of M and some diagonal metric on the holonomy algebra corresponding to \(\Lambda \).

中文翻译：

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关于不变度量连接的爱因斯坦-杨-米尔斯洛伦兹对称空间

我们用爱因斯坦-杨-米尔斯方程组的连通非平各向同性群提供解对四维连通简单连通的洛伦兹对称空间M进行分类。这些解决方案是针对M正交框架束中的某些不变度量连接\（\ Lambda \）和与\（\ Lambda \）对应的完整代数上的一些对角度量而构建的。