This award supports research on enveloping algebras, differential operators and quantum groups. The principal investigator will study primitive ideals in the enveloping algebra of a classical Lie superalgebra. He will also study links in multiparameter quantum function algebras and the coradical filtration for the corresponding enveloping algebras. The goal is to understand the structure of certain Hopf algebras arising in the theory of quantum groups. Finally, the principal investigator will study the K-theory of differential operators of toric varieties. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication defined on it. Although the additive operation satisfies the commutative law, the multiplicative operation is not required to do so. An example of a ring for which multiplication in not commutative is the collection of nxn matrices over the integers. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.
