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

该基金支持Costa和Keller教授研究环上线性、经典和Chevalley群的正规子群。他们想把对特殊线性群和自旋群已经得到的结果推广到B、G和F型线性群。他们还打算研究局部域上特殊的2维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性的研究。因此，这一领域直接应用于物理和化学的许多领域。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。也有直接联系的纠错码是至关重要的现代计算，如与光盘的工作，以及理论计算机科学的一般。

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.