The structure of almost connected pro-lie groups

Title: The structure of almost connected pro-lie groups
Creator: Hofmann, Karl; Morris, Sidney
Date: 2011
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/69355
Identifier: vital:4080
Identifier: ISSN:0949-5932
Abstract: Recalling that a topological group G is said to be almost connected if the quotient group G=G0 is compact, where G0 is the connected component of the identity, we prove that for an almost connected pro-Lie group G, there exists a compact zero-dimensional, that is, profinite, subgroup D of G such that G = G0D. Further for such a group G, there are sets I , J , a compact connected semisimple group S , and a compact connected abelian group A such that G and ℝI × (ℤ=2ℤ)J × S × A are homeomorphic. En route to this powerful structure theorem it is shown that the compact open topology makes the automorphism group Aut g of a semisimple pro-Lie algebra g a topological group in which the identity component (Aut g)0 is exactly the group Inn g of inner automorphisms. In this situation, Inn(G) has a totally disconnected semidirect complement
Relation: Journal of Lie Theory Vol. 21, no. 2 (2011), p. 347-383
Rights: Copyright Heldermann Verlag
Rights: This metadata is freely available under a CCO license
Subject: 0101 Pure Mathematics; Almost connected; Conjugacy of subgroups; Maximal compact subgroup; Pro-lie group
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