According to Skolem’s conjecture, if an exponential Diophantine equation is not solvable, then it solvable modulo appropriately chosen modulus. Besides several concrete equations, the conjecture has only been proved for rather special cases. In

We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov structure. We use extensions and classical r-matrices to construct Novikov structures on certain classes of solvable Lie algebras.