We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by Killing spinors in all dimensions. We show that bilinears of geometric Killing spinors produce special Killing–Yano forms and special conformal Killing–Yano forms. After defining the Lie algebra structure of hidden symmetries generated by Killing spinors, we construct symmetry operators as the generalizations of the Lie derivative on spinor fields. All these constructions together constitute the structure of generalized symmetry superalgebras. We exemplify the construction on weak G₂ and nearly Kähler manifolds.

中文翻译：

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广义对称超级代数

我们将流形上的等距和几何 Killing 旋量的对称超代数推广到包括所有维度中 Killing 旋量生成的流形的所有隐藏对称性。我们证明几何 Killing 旋量的双线性产生特殊的 Killing-Yano 形式和特殊的保形 Killing-Yano 形式。在定义了 Killing spinor 生成的隐藏对称的 Lie 代数结构之后，我们构造了对称算子作为 Lie 导数在 Spinor 场上的推广。所有这些构造共同构成了广义对称超代数的结构。我们举例说明弱G ₂和近 Kähler 流形的构造。