Mathematical Sciences: "Cocharacter Sequences"

9622062 Berele This award supports the research of Professor A. Berele to work in non-commutative ring theory with special emphasis on problems arising from generalizations of the theory of cocharacter sequences that arise in the study of p.i. algebras. In particular, he wants to study cocharacter sequences that arise from Hopf algebra actions. This is research in the subfield of algebra called non-commutative ring theory. Algebra can be though of as the study of symmetry in the abstract. As such, algebra has direct applications to areas of physics and chemistry. In fact, much of non-commutative ring theory generalizes structures found in Quantum Mechanics and this proposal continues to explore areas that connect directly with modern quantum field theory. There are also connections to problems in many other areas of mathematics such as invariant theory.