Lie Algebroids and Lie Pseudoalgebras

Lie algebroids and Lie pseudoalgebras arise from a wide variety of constructions in differential geometry; they have been introduced repeatedly into the geometry, physics and algebra literatures since the 1950s, under some 14 different terminologies. The first main part (Sections 2–5) of this survey describes the four principal classes of examples, emphazising that each arises by means of a generalization of the Lie theory of Lie groups and Lie algebras; this part is addressed primarily to those interested in differential geometry. The second part (Sections 7–8), addressed equally to algebraists, describes various algebraic constructions currently known for Lie algebroids and Lie pseudoalgebras, and their geometric significance.