Symmetries and supersymmetries of the Dirac-type operators on curved spaces

Abstract:
The continuous and discrete symmetries of the Dirac-type operators constructed with Killing-Yano tensors are studied in manifolds of arbitrary dimensions. The covariantly constant Killing-Yano tensors realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. The briefly presented examples are the Euclidean Taub-NUT space and Minkowski spacetime.

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