Mathematical Sciences: Linear, Classical, and Chevalley Groups Over Rings

该基金支持Costa和Keller教授对环上线性群、经典群和Chevalley群的正规子群的研究。他们想把已经得到的关于特殊线性群和自旋群的结果推广到B型、G型和f型线性群。他们还想研究局域上2维特殊线性群的子群与希尔伯特符号之间的关系。这是代数领域的研究。这个领域可以被认为是对抽象对称的研究。因此，这个领域对物理和化学的许多领域都有直接的应用。此外，在过去的30年里，许多与数据传输问题有关的问题已经用群论的技术解决了。它还与纠错码有直接的联系，纠错码对现代计算至关重要，比如使用CD-ROM以及一般的理论计算机科学。

This grant supports the research of Professors Costa and Keller to study the normal subgroups of the linear, classical and Chevalley groups over rings. They want to extend the results already obtained for the special linear and spin groups to the linear groups of type B, G and F. They also intend to study the relationship between subgroups of the special linear group of dimension 2 over a local field and Hilbert symbols. This is research in the field of algebra. This area can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's as well as to theoretical computer science in general.