On the order reduction of differential invariants

Michal Krupka

Abstract. The notion of a basis of differential invariants (natural mappings)
is discussed. A formula is shown determining a basis of invariants of
arbitrary order by means of the lowest order basis of invariants. As an
example, all invariants of $n$-tuples of vector fields are determined. It is
shown that each such a differential invariant is generated by the Lie bracket.

Keywords: jet, velocity, differential group, prolongation of a jet bundle,
differential invariant, basis of invariants, Lie bracket.

MS classification: 58A20, 53A55.