The Journal of Geometric Mechanics (JGM)

Models for higher algebroids

Pages: 317 - 359, Volume 7, Issue 3, September 2015      doi:10.3934/jgm.2015.7.317

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Michał Jóźwikowski - Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland (email)
Mikołaj Rotkiewicz - Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland (email)

Abstract: Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie algebroid. A higher algebroid is, in principle, a graded bundle equipped with a differential relation of special kind (a Zakrzewski morphism). In the paper we investigate basic properties of higher algebroids and present some examples.

Keywords:  Higher algebroids, almost Lie algebroids, graded bundles, reduction of Lie groupoids.
Mathematics Subject Classification:  Primary: 58A20, 58A50; Secondary: 70G65, 70H50.

Received: June 2013;      Revised: June 2015;      Available Online: July 2015.