  Generalized Schouten, Froelicher-Nijenhuis and Froelicher-Richardson brackets
are defined for an arbitrary Lie algebroid. Tangent and cotangent lifts of Lie
algebroids are introduced and discussed and the behaviour of the related graded
Lie brackets under these lifts is studied. In the case of the canonical Lie
algebroid on the tangent bundle, a new common generalization of the
Froelicher-Nijenhuis and the symmetric Schouten brackets, as well as embeddings
of the Nijenhuis-Richardson and the Froelicher-Nijenhuis bracket into the
Schouten bracket, are obtained.
