Hopf Algebras

9401324尼科尔斯该奖项支持Hopf代数研究方面的基础性工作。项目的主要目标是解决关于Hopf代数的Kaplansky的第六个猜想——对于在代数闭域上定义的有限维的半简单Hopf代数H，每个简单右H模的维数除以H的维数。主要研究者还将研究与Hopf代数工作相关的一些涉及符号计算的问题。本研究涉及一种称为Hopf代数的代数对象。虽然这个领域是相当技术性的，但霍普夫代数正变得越来越有兴趣，甚至对非数学家来说也是如此。Hopf代数在分子化学家感兴趣的结理论中很有用。某些类型的霍普夫代数现在被称为量子群，以表彰它们在物理学中的应用。Hopf代数用于研究微分算子，使组合学更像微积分。

9401324 Nichols This award supports fundamental work on the study of Hopf algebras. The main goal of the project is the solution of Kaplansky's sixth conjecture on Hopf algebras--for a finite dimensional cosemisimple Hopf algebra H defined over an algebraically closed field, the dimension of every simple right H-comodule divides the dimension of H. The principal investigator will also study some questions involving symbolic computation which have arisen in connection with the Hopf algebra work. This research is concerned with an algebraic object called a Hopf algebra. While the area is quite technical, Hopf algebras are becoming of increasing interest, even to non mathematicians. Hopf algebras are useful in the type of knot theory that is of interest to molecular chemists. Certain types of Hopf algebras are now referred to as quantum groups in recognition of their applications in physics. Hopf algebras are used to study differential operators and to make combinatorics more like calculus.