Über Algebren mit nilpotenten assoziierten Lie-Ringen
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and the Hamiltonian operators in formal variational calculus. In this note we prove that the underlying Lie algebras of quadratic Novikov algebras are 2-step nilpotent. Moreover, we give the classification up to dimension .
We prove that the Lie algebra of infinitesimal automorphisms of the transverse structure on the total space of the transverse bundle of a foliation is isomorphic to the semi-direct product of the Lie algebra of the infinitesimal automorphism of the foliation by the vector space of the transverse vector fields. The derivations of this algebra are entirely determined and we prove that this Lie algebra characterises the foliated structure of a compact Hausdorff foliation.