We derive a necessary and sufficient condition for Poincaré Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the Schur group on the vector space of superbrackets. We then classify four-dimensional [Formula: see text] supersymmetry algebras, which are found to be unique in Euclidean and in neutral signature, while in Lorentz signature there exist two algebras with R-symmetry groups [Formula: see text] and [Formula: see text], respectively.

中文翻译：

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任意签名中的四维向量多重态（一）

我们推导出任何维度和签名的庞加莱李超代数同构的充分必要条件。这减少了分类问题，直到某些离散操作，才能在超括号的向量空间上对 Schur 群的轨道进行分类。然后我们对四维[公式：见文本]超对称代数进行分类，发现它们在欧几里得和中性签名中是唯一的，而在洛伦兹签名中存在两个具有 R 对称群的代数 [公式：见文本] 和 [公式：见正文]，分别。