Representational Theory of Infinite Dimensional Lie (super) Algebras and Related Algebraic Structures

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

The project is concentrated around the following topics: 1.Conformal superalgebra encodes an axiomatic description of the operator product expansion in conformal field theory. 2.Representation theory of finite Lie pseudoalgebras. The next goal is representation theory of finite simple Lie pseudoalgebras and the corresponding cohomology theory. 3.Representation theory of linearly compact Lie superalgebras and the Standard Model. The next challenge is to build their representation theory. 4.Integrable representations of affine superalgebras and near modular functions. This is a proposal in the area of mathematics known as Lie Algebras. Lie algebras are one of the tools mathematicians use to study all kinds of symmetries that occur in nature. In recent years, infinite-dimensional Lie algebras have been used to describe the symmetries of subatomic particles. The main objective of the project is to explore connections of the theory of infinite-dimensional symmetries to other fields of mathematics and to theoretical physics. It is hoped that this will lead to a better understanding of the structure of quarks and leptons