On a class of local Lie algebras over a manifold
Abstract
This letter presents a study of the automorphisms and the derivations of a large class of local Lie algebras over a manifold M (in the sense of Shiga and Kirillov) called Lie algebras of order O over M. It is shown that, in general, the algebraic structure of such an algebra Г characterizes the differentiable structure of M and that the Lie algebra of derivations of Г is a Lie algebra of differential operators of order 1 over M obtained in a natural way as the space of sections of a vector bundle canonically associated to Г.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 September 1979
 DOI:
 10.1007/BF00397214
 Bibcode:
 1979LMaPh...3..405L