This award is concerned with the study of algebras with trace functions and their trace identities. Of special interest are associated universal algebras and their Poincare series. Invariant theory will be an important tool. The principal investigator is interested in determining why so many universal polynomial identity algebras with trace occur as fixed rings for important groups, Lie algebras and super Lie algebras. 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 is 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.
