XXXVI Workshop on Geometric Methods in Physics | 2-8.07.2017 |

VI School on Geometry and Physics | 26-30.06.2017 |

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## Bogdan Balcerzak## On Dirac type operators determined by skew-symmetric 2-tensors on anchored vector bundlesDirac type operators on anchored vector bundles (in particular on Lie algebroids) with respect to skew-symmetric 2-tensors will be defined and discussed. Classical Dirac operators are determined by the Clifford algebra structures and connections, whilst considered Dirac type operators are determined by the Weyl algebras (the skew-symmetric counterpart of Clifford algebras) and connections. The Clifford algebra structures come from symmetric 2-tensors (eg. pseudo-Riemannian tensors), whereas the Weyl algebra structures are given by skew-symmetric 2-tensors (eg. by symplectic forms) or bivectors (eg. Poisson structures) on the given vector bundle or on its dual. |

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University of Bialystok |

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