Totally Disconnected Groups and their Automorphism

完全不连通群及其自同构

• 批准号: 43659331
• 负责人: Professor Dr. Helge Glöckner
• 金额: --
• 依托单位: Fachgebiet Unendlich-dimensionale Analysis und Geometrie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/43659331?language=en
• 关键词: Totally; Disconnected; Groups; their; Automorphism

While specific classes of totally disconnected, locally compact topological groups (like profinite groups, automorphism groups of graphs and linear algebraic groups over local fields) have been studied successfully for a long time with specific tools, a structure theory for general totally disconnected groups only developed in the 1990s after a seminal paper by George A. Willis (Newcastle, N.S.W., Australia). The current project intends to enable further cooperation between G. A. Willis and the applicant, complemented by funding from the Australian side. Its goals are twofold:1. To develop further the structure theory of totally disconnected groups and their automorphisms, notably to obtain further insight into the contraction groups associated with automorphisms.2. To extend results previously only known for p-adic Lie groups and their automorphisms to the case of Lie groups over local fields of positive characteristic, using ideas from the general structure theory.

虽然特定类别的完全不连通，局部紧拓扑群（如profinite群，图的自同构群和局部域上的线性代数群）已经成功地研究了很长一段时间，但一般完全不连通群的结构理论直到20世纪90年代才在乔治A.威利斯（纽卡斯尔，N. S.W.，澳大利亚）。目前的项目旨在使G. A.威利斯和申请人，由澳方资助的补充。它的目标有两个：1。进一步发展了完全不连通群及其自同构的结构理论，特别是对与自同构相关的压缩群有了进一步的认识。利用一般结构理论的思想，把以前只知道的关于p-adic李群及其自同构的结果推广到局部正特征域上李群的情况。