Continuity of π‐Perfection for Compact Lie Groups
Continuity of π‐Perfection for Compact Lie Groups
复制标题
紧李群的 π 完美连续性
DOI：
10.1112/s0024609304003601
复制
发表时间：
2005
影响因子：
0.9
通讯作者：
B. Oliver
中科院分区：
文献类型：
--
作者：
H. Fausk;B. Oliver
设G是紧李群，π是任意素数或素数集。构造了一个“π-完美映射”：即从G的所有闭子群的共轭类空间到π-完美子群的共轭类空间的一个连续函数，π-完美子群在它们的正规化子中具有有限指数。这是用来证明局部化在π上的G的伯恩赛德环的幂等元与G的π-完全子群的共轭类空间的开子集和闭子集是双射对应的，其中π-完全子群在它们的正规化子中具有有限指数。2000年数学学科分类55 P91（小学）。
Let G be a compact Lie group, and let π be any prime or set of primes. A ‘π‐perfection map’ is constructed: that is, a continuous function from the space of conjugacy classes of all closed subgroups of G to the space of conjugacy classes of π‐perfect subgroups with finite index in their normalizer. This is used to show that the idempotent elements of the Burnside ring of G localized at π are in bijective correspondence with the open and closed subsets of the space of conjugacy classes of π‐perfect subgroups of G with finite index in their normalizer. 2000 Mathematics Subject Classification 55P91 (primary).