A classical construction of Atiyah assigns to a (real or complex) Lie group G and principal G bundle P over a manifold M, a Lie algebroid over M. The spirit behind our work is to put this work within an algebraic context, replace M by a scheme X and G by a ”simple” reductive group scheme over X (in the sense of Demazure-Grothendieck) that arise naturally with an attached torsor (which plays the role of P) in the study of Extended Affine Lie Algebras. Lie algebroids in an algebraic sense were also considered by Beilinson and Bernstein. We will explain how the present work relates to theirs. This is joint work with J. Kuttler and F. Quallbrunn.
