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.

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).当前的项目旨在使G. A. Willis与申请人之间进行进一步的合作，并通过澳大利亚方面的资金进行补充。它的目标是双重的：1。为了进一步发展完全断开的群体及其自动形态的结构理论，特别是为了进一步了解与自动形态相关的收缩群体。2。为了扩展以前仅针对P-Adic Lie群体及其自动形态闻名的结果，使用一般结构理论的思想，将谎言群体的谎言群体列为谎言群体。