Mathematical Sciences: "Cocharacter Sequences"

9622062贝雷勒该奖项支持A.贝雷勒教授致力于非对易环论的研究，特别强调在P.I.研究中出现的由余字序列理论的推广所引起的问题。代数。特别是，他想研究由Hopf代数作用产生的余字符序列。这是代数子领域的研究，称为非对易环论。代数可以看作是对抽象对称性的研究。因此，代数在物理和化学领域有直接的应用。事实上，许多非对易环理论概括了量子力学中发现的结构，该提议继续探索与现代量子场论直接相关的领域。它还与数学的许多其他领域的问题有联系，例如不变量理论。

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.