Mathematical Sciences: Noncommutative Projective Geometry

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This research is concerned with noncommutative algebra, particularly the theory of noncommutative noetherian rings and its applications to other areas of mathematics. The principal investigator will study the abstract properties of nontrivial examples and their interrelationship with the theory of quantum groups. He will also consider the skew group ring of a finite group acting on a polynomial ring to determine when the category of projective modules over such a ring satisfies cancellation. The postdoctoral associate will study the stable rank of enveloping algebras of semisimple Lie algebras. 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. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.