Abstract We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat left-invariant Einstein metrics in both the class of metrics for which the nice basis is orthogonal and a more general class associated to order two permutations of the nice basis. We obtain classifications in dimension 8 and, under the assumption that the root matrix is surjective, dimension 9; moreover, we prove that Einstein nilpotent Lie groups of nonzero scalar curvature exist in every dimension ≥8\geq 8.

中文翻译：

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好的李群上的不定爱因斯坦度量

摘要 我们介绍了一种系统的方法来在好的幂零李群上产生不定签名的左不变、非 Ricci-flat 爱因斯坦度量。在一个 nice 幂零李群上，我们给出了一个简单的非 Ricci-flat 左不变爱因斯坦度量的代数表征，其中包括 nice 基正交的度量类和一个更一般的类，用于对 nice 的两个排列进行排序基础。我们在维度 8 中获得分类，并且在根矩阵是满射的假设下，维度为 9；此外，我们证明了非零标量曲率的爱因斯坦幂零李群存在于每个维度≥8\geq 8。