This project is concerned with the representation theory of algebraic groups and Lie algebras. The spectrum of the cohomology ring will be a fundamental object of interest. This will enable the principal investigator to apply methods from algebraic geometry and algebraic topology in order to understand the representation/cohomology theory of these groups and algebras. The research supported concerns the representation theory of various algebraic objects including algebraic groups and Lie algebras. Representation theory is an important method for determining the structure of these objects. This work has important implications for a number of areas of mathematics including ring theory, group theory, topology and the study of Lie algebras.
