On the structure of finite Novikov conformal algebras

We describe finite simple Novikov conformal algebras over an algebraically closed field of characteristic zero. The classification includes the current conformal algebra over the base field and a one-parameter list of Virasoro-like conformal algebras. A semisimple finite Novikov conformal algebra is proved to be a direct sum of simple ones. We also describe deformations and central extensions of finite simple Novikov conformal algebras.