Representation Theory of Non-graded, Non-restricted Modular Lie algebras

Abstract

We classify in a uni ed approach the simple restricted modules for the minimal p-envelope of the non-graded, non-restricted Hamiltonian Lie algebra H.2I.1; 1/I ˆ.1// over an algebraically closed eld k of characteristic p 5. We also give the restrictions of these modules to a subalgebra isomorphic to the rst Witt Algebra, a result stated in [S. Herpel and D. Stewart, Selecta Mathematica 22:2 (2016) 765–799] with an incomplete proof. We end by completing the classi cation of the simple restricted modules over elds of all characteristics by considering the characteristic 3 case separately