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.
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Lecomte, P. On a class of local Lie algebras over a manifold. Lett Math Phys 3, 405–411 (1979). https://doi.org/10.1007/BF00397214
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DOI: https://doi.org/10.1007/BF00397214