Loop algebras of Zassenhaus algebras in characteristic three

The simple, modular Lie algebras of Zassenhaus have peculiar features in ch aracteristic three. Their second cohomology groups are larger than in chara cteristic p > 3, and they possess a non-degenerate associative form. These properties are reflected in the presentations of certain loop algebras of t hese algebras, that arise naturally in analogy with the graded Lie algebra associated to the Nottingham group with respect to its lower central series .