Continuity of π‐Perfection for Compact Lie Groups | Zendy

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Continuity of π‐Perfection for Compact Lie Groups

Author(s) -

Fausk Halvard,

Oliver Bob

Publication year - 2005

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609304003601

Subject(s) - mathematics , conjugacy class , bijection , centralizer and normalizer , pure mathematics , prime (order theory) , space (punctuation) , combinatorics , philosophy , linguistics

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).

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