Linear algebraic groups and related topics in algebra

线性代数群和代数中的相关主题

• 批准号: 1201542
• 负责人: Parimala Raman
• 金额: $ 14.13万
• 依托单位: Emory University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1201542&HistoricalAwards=false
• 关键词: Linear; algebraic; groups; related; topics

The PI proposes to exploit recently developed techniques in the study of projective homogeneous varieties to pursue several questions in the theory of semisimple algebraic groups over an arbitrary field, their Galois cohomology, and their cohomological invariants. The new techniques have already produced some extremely strong results and the investigator proposes to push them further. Previous work on these topics has had applications to other areas of mathematics and to physics, and further such applications are expected.The family of semisimple groups includes familiar matrix groups like special linear and special orthogonal groups. These groups appear in many areas of mathematics, and may be viewed as an essential outgrowth of the linear algebra developed in the early 1800s and now taught to undergraduates. The groups became prominent objects of mathematical interest in the late 1800s via Sophus Lie's famous general theory of Lie groups. In algebra, the notion of semisimple group unifies various historically distinct areas of study. For example, it connects Jordan algebras -- discovered by physicists -- with quadratic forms and division algebras.

PI提议利用最近开发的技术在研究射击均质品种的研究中，以在任意领域，GALOIS的共同体学及其共同体学理论中提出几个问题。 新技术已经产生了一些非常强大的结果，研究人员建议将它们进一步推动。 这些主题的先前工作已应用于其他数学领域和物理学领域，并且预计会有进一步的应用。半杂志组的家族包括熟悉的矩阵组，例如特殊线性和特殊正交组。这些群体出现在数学的许多领域中，可能被视为在1800年代初期开发的线性代数的重要产物，现在教导了本科生。在1800年代后期，通过Sophus Lie著名的谎言群体理论，这些团体成为数学兴趣的重要对象。在代数中，半圣像组的概念统一了各种历史上不同的研究领域。例如，它将物理学家发现的Jordan代数与二次形式和分区代数联系起来。