Models for higher algebroids

Michał  Jóźwikowski; Mikołaj Rotkiewicz

doi:10.3934/jgm.2015.7.317

Article Contents

2015, Volume 7, Issue 3: 317-359. Doi: 10.3934/jgm.2015.7.317

This issue Previous Article Lie algebroids generated by cohomology operators Next Article The emergence of torsion in the continuum limit of distributed edge-dislocations

Models for higher algebroids

Michał Jóźwikowski^1, and
Mikołaj Rotkiewicz^2,

1.
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa
2.
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa

Received: June 2013

Revised: June 2015

Published: September 2015

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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:

Mathematics Subject Classification: Primary: 58A20, 58A50; Secondary: 70G65, 70H50.

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