On Finite-Dimensional Simple Novikov Algebras of Characteristic $ p $

Abstract

Let \( N \) be a nonassociative finite-dimensional simple Novikov algebra over an algebraically closed field \( F \) of characteristic \( p>0 \). Then the right multiplication algebra \( R \) is a differential simple algebra with respect to some derivation \( d \). The algebra \( N \) is isomorphic to a Novikov algebra \( (R,d,R_{x}) \) for some operator of right multiplication by \( x \) and multiplication is given by \( u\circ w=ud(w)+R_{x}uw \). Moreover, the algebra \( R \) is a truncated polynomial algebra.