Mathematical Sciences: Finite Subgroups of Lie Groups and Automorphisms of Vertex Operator Algebras

小行星9623038 该基金支持R教授的研究。格里斯在三个不同的领域工作。第一个领域是将有限单群嵌入某些例外李群。接下来他将研究无穷维顶点算子代数的自同构群。最后，他希望拿出的方法，将给予一个更统一的方法产生的有限简单的群体通过研究自同构的某些格。 这是代数领域的研究。代数可以被认为是抽象的对称性的研究。因此，代数在物理和化学领域有直接的应用。特别是现代理论的规范场在物理学中广泛使用这一领域的代数。还有编码理论和跨通信线路的数据传输。

9623038 Griess This grant supports the research of Professor R. Griess to work on three different areas. The first area is that of embedding finite simple groups into certain exceptional Lie groups. Next he will study the automorphism groups of infinite dimensional vertex operator algebras. Finally he hopes to come up with methods that will give a more uniform method of generating the finite simple groups through the study of automorphisms of certain lattices. This is research in the field of algebra. Algebra can be thought of as the study of symmetry in the abstract. As such algebra has direct applications to areas of physics and chemistry. In particular the modern theory of gauge fields in physics uses this area of algebra extensively. There are also connections to coding theory and the transmission of data across communication lines.