An algebra is called Novikov if and for all . The author gives a complete classification of finite-dimensional simple Novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic . (In particular, if is a finite-dimensional simple Novikov algebra over , then for some positive integer there is a basis for such that
where , are constants. (Here if The author also introduces what he calls “Novikov-Poisson algebras” and their tensor theory. All of this builds on the results in a number of articles by J. M. Osborn.