Distributions and quotients on degree 1 NQ-manifolds and Lie algebroids
arXiv:1202.1378
Abstract
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.
Our previous submission arXiv:1012.0428v1 has been divided into two papers. The present paper contains sections 1.3 and 4 (improved in their presentation), and additionally addresses the link to IM-foliations. 19 pages