Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 135, 46 pages      arXiv:1708.03174      https://doi.org/10.3842/SIGMA.2018.135

Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms

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

Received January 10, 2018, in final form December 12, 2018; Published online December 29, 2018

Abstract
We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a special kind. In our approach higher algebroids are vector bundle comorphism between graded-linear bundles satisfying natural axioms. We provide natural examples and discuss applications in geometric mechanics.

Key words: higher algebroid; vector bundle comorphism; almost-Lie algebroid; graded manifold; graded bundle; algebroid lift; variational principle.

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