Enright will study the representation theory of Lie algebras defined over a commutative ring in a setting where a distinguished maximal ideal is proscribed for which the residue field is the complex numbers. Of particular interest is whether information at the level of Lie algebras defined over rings yield important information for the more traditional Lie algebras defined over the complex numbers by passage from the ring to the residue field. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.
