DISTRIBUTIONS AND QUOTIENTS ON DEGREE NQ-MANIFOLDS AND LIE ALGEBROIDS.

It is well-known that a Lie algebroid A is equivalently described by a degree 1 NQ-manifold ϻ. We study distributions on ϻ, giving a characterization in terms of A. We show that involutive Q-invariant distributions on ϻ 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 ϻ. [ABSTRACT FROM AUTHOR]