The Lie algebra of a Lie algebroid (Q2782563)

The authors consider a commutative and unitary ring (respectively, a field) \({\mathcal R}\), a commutative and unitary \({\mathcal R}\)-algebra \({\mathcal A}\) and a Lie pseudoalgebra \({\mathcal L}\) over \({\mathcal R}\) and \({\mathcal A}\). Then, under certain conditions of regularity, they describe the maximal Lie ideals of \({\mathcal L}\) (respectively, the maximal finite-codimensional Lie subalgebras of \({\mathcal L}\)) in terms of the maximal \({\mathcal L}\)-invariant ideals of \({\mathcal A}\) (respectively, the maximal finite-codimensional ideals of \({\mathcal A}\)). As a consequence, they deduce a Pursell-Shanks type theorem [\textit{M. Shanks} and \textit{L. Pursell}, Proc. Am. Math. Soc. 5, 468-472 (1954; Zbl 0055.42105)] for Lie algebroids with non-singular anchor maps.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00030].