Leibniz algebras in characteristic [formula omitted

Abstract

We give the definition of restrictness for Leibniz algebras in characteristic p. We prove that the cohomology of Leibniz algebras with coefficients in an irreducible module is trivial, if the module is not restricted. The number of irreducible antisymmetric modules with nontrivial cohomology is finite. A Leibniz algebra is called simple, if it has no proper ideal except ideal generated by squares of its elements. We describe simple Leibniz algebras with Lie factor isomorphic to sl 2 and p m -dimensional Zassenhaus algebra W 1(m) .