Remarks on the Schouten-Nijenhuis bracket
Source file as Portable Document Format Postscript Document

Peter Michor

The paper is published: Rendiconti del Circolo Matematico di Palermo, Serie II, , Suppl. 16 (1987), 208--215

MSC 2000

53A55 Differential invariants (local theory), geometric objects

A global definition of the Schouten bracket is given, and a global proof of its connection to Poisson structures on manifolds. Some properties are derived, in particular naturality. Then all natural bilinear concomitants of multi vector fields with the same degree behavior as the Schouten Nijenhuis bracket are determined: only constant multiples of the Schouten-Nijenhuis bracket appear.

Keywords: Schouten-Nijenhuis bracket, Schouten bracket

The methods of proof were later explained in the book: Kolar, Ivan; Michor, Peter W.; Slovak, Jan Natural operations in differential geometry. (English) Berlin: Springer-Verlag. vi, 434 p. (1993). The results are cited but not proved.