XXXIX Workshop on Geometric Methods in Physics 27.06-3.07.2021
IX School on Geometry and Physics 21-25.06.2021

Ümit Ertem

Generalized symmetry superalgebras

Killing vector fields and geometric Killing spinors together form a symmetry superalgebra structure on a spin manifold. We generalize these symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by geometric Killing spinors in all dimensions. Hidden symmetries of a manifold correspond to antisymmetric generalizations of Killing vector fields to higher-degree differential forms and are called Killing-Yano forms. We show that bilinear forms of geometric Killing spinors produce special Killing-Yano and special closed conformal Killing-Yano forms. After defining the Lie algebra structure of hidden symmetries generated by geometric Killing spinors, we construct the symmetry operators as the generalizations of the Lie derivative on spinor fields. All these constructions constitute the structure of generalized symmetry superalgebras.

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of Bialystok
University of Bialystok

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