Modular Lie algebras and representation theory

The project concerns the theory of Lie algebras over fields of positive characteristic. Given the Lie algebra of a reductive algebraic group, we will consider questions about subalgebras containing a given nilpotent element. A fundamental question is to determine the subalgebras isomorphic to the special linear Lie algebra, and we plan to make progress understanding such subalgebras for restricted nilpotent elements. Further investigation will be made in to the smallest simple restricted subalgebra containing a nonrestricted nilpotent element. Subsequently, we plan to make progress in understanding all semisimple subalgebras containing a nilpotent elements in large orbits.

The methods will involve the representation theory of modular Lie algebras and cohomology of representations. In the case of groups of classical type, the natural representation and the theory of Jordan normal form will be employed, whereas computational methods may be used for the case of groups of exceptional type.

EPSRC subject area: Algebra