Distributions and quotients on degree 1 NQ-manifolds and Lie algebroids

Details Distributions and quotients on degree 1 NQ-manifolds and Lie algebroids Distributions and quotients on degree 1 NQ-manifolds and Lie algebroids

2012-02-07

arxiv.org/abs/1202.1378v1

Mathematics

Differential Geometry

Our previous submission arXiv:1012.0428v1 has been divided into two papers. The present paper contains sections 1.3 and 4 (imp

Scientific paper

It is well-known that a Lie algebroid A is equivalently described by a degree 1 Q-manifold M. We study distributions on M, giving a characterization in terms of A. We show that involutive Q-invariant distributions on M correspond bijectively to IM-foliations on A (the infinitesimal version of Mackenzie's ideal systems). We perform reduction by such distributions, and investigate how they arise from non-strict actions of strict Lie 2-algebras on M.

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