XXXII Workshop on Geometric Methods in Physics | 30.06-6.07.2013 |

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## Mikołaj Rotkiewicz## Higher algebroids and reductions of higher tangent bundlesI will show how to define objects called {\it higher (Lie) algebroids} which generalize higher tangent bundles $T^kM$ in the same way as (Lie) algebroids generalize the tangent bundle $TM$. I will study the reductions of higher tangent bundles of a Lie groupoid which provide a natural example of such objects. Then I will give an abstract definition of higher algebroids taking an arbitrary almost Lie algebroid as a starting point. This higher version of algebroids is suitable for geometric framework for variational problems in which Lagrangian depends on higher derivatives and has some inner symmetries. My talk is based on a joint paper with Michał Jóźwikowski. |

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University of Bialystok |

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