JACOBI STRUCTURES REVISITED

JANUSZ GRABOWSKI

Abstract. A lifting procedure of first-order multi-differential operators is defined which maps the Nijenhuis-Richardson into the Schouten bracket. This is a way of associating canonically a Lie algebroid with any local Lie algebra structure on a 1–dimensional vector bundle.

Mathematical Institute, Polish Academy of Sciences ul. Śniadeckich 8 P.O. Box 137, 00-950 Warszawa POLAND e-mail: jagrab@mimuw.edu.pl