XXXVI Workshop on Geometric Methods in Physics 2-8.07.2017
VI School on Geometry and Physics 26-30.06.2017

Bogdan Balcerzak

On Dirac type operators determined by skew-symmetric 2-tensors on anchored vector bundles

Dirac 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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Centre de recherches mathématiques          University
of Bialystok
University of Bialystok

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