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

SIGMA 11 (2015), 079, 16 pages      arXiv:1412.5981      https://doi.org/10.3842/SIGMA.2015.079
Contribution to the Special Issue on Poisson Geometry in Mathematics and Physics

Lie Algebroids in the Loday-Pirashvili Category

Ana Rovi ab
a) School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK
b) School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK

Received February 27, 2015, in final form September 28, 2015; Published online October 02, 2015

Abstract
We describe Lie-Rinehart algebras in the tensor category $\mathcal{LM}$ of linear maps in the sense of Loday and Pirashvili and construct a functor from Lie-Rinehart algebras in $\mathcal{LM}$ to Leibniz algebroids.

Key words: Lie algebroid; Leibniz algebra; Courant algebroid; Leibniz algebroid.

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