XXXII Workshop on Geometric Methods in Physics 30.06-6.07.2013

Mikołaj Rotkiewicz

Higher algebroids and reductions of higher tangent bundles

I 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.

Event sponsored by:
Belgian Science Policy Office     PAI          University
of Bialystok
University of Bialystok

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