Asyptoptic and Combinatorial Methods in Infinite Groups and Algebras

无限群和代数中的渐近方法和组合方法

• 批准号: 0758487
• 负责人: Efim Zelmanov
• 金额: $ 61.06万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0758487&HistoricalAwards=false
• 关键词: Asyptoptic; Combinatorial; Methods; Infinite; Groups

The proposal focuses on infinite dimensional algebras and infinite residually finite groups and their interactions. We plan to study the recently discovered families of Lie algebras of infinite differential operators over fields of positive characteristics which are both nil and of polynomial growth. We intend to continue our work on asymptotic properties of Golod-Shafarevich groups and the Lubotzky-Sarnak conjecture. These groups naturally arise in 3-dimensional topology and number theory. This work is also related to the Wigderson's problem of expanding subspaces in the theoretical computer science. We will further develop the connections between the Specht Problem and linear representations of Golod-Shafarevich groups.We hope that the results of the work on the proposal will lead to solutions of several long standing problems and will haveimplications for Theoretical Computer Science (fast expanding systems).

该建议集中于无限维代数和无限剩余有限群及其相互作用。我们计划研究最近发现的关于正特征域上无限微分算子族的李代数族，正特征域既是零的，又是多项式增长的。我们打算继续研究Golod-Shafarevich群和Lubotzky-Sarnak猜想的渐近性质。这些群自然出现在三维拓扑学和数论中。这项工作也与维格德森在理论计算机科学中扩张子空间的问题有关。我们将进一步发展Speht问题与Golod-Shafarevich群的线性表示之间的联系。我们希望关于该提议的工作的结果将导致几个长期存在的问题的解决，并将对理论计算机科学(快速扩展系统)产生影响。