Pro-Lie Groups
نویسندگان
چکیده
منابع مشابه
A Note on Pro-lie Groups
We give a short proof of the theorem that a closed subgroup of a countable product of second countable Lie groups is pro-Lie. The point of this note is to give a short and self-contained, modulo well known results, proof of a theorem of Hofmann and Morris [3] (see also [4, Theorem 3.35] and [5]) in the case of second countable groups. Another simple proof of the result of Hofmann and Morris was...
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We are concerned with conditions under which a locally compact group G has a maximal compact normal subgroup K and whether or not G/K is a Lie group. If G has small compact normal subgroups K such that G/K is a Lie group, then G is pro-Lie. If in G there is a collection of closed normal subgroups {Ha} such that f~| Ha = e and G/Ha is a Lie group for each a, then G is a residual Lie group. We de...
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A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete category. It includes each finite-dimensional Lie group, each locally-compact group that has a compact quotient group modulo its identity compo...
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These notes are an introduction to Lie algebras, algebraic groups, and Lie groups in characteristic zero, emphasizing the relationships between these objects visible in their categories of representations. Eventually these notes will consist of three chapters, each about 100 pages long, and a short appendix. Single paper copies for noncommercial personal use may be made without explicit permiss...
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Example 1.3. (R,+) Example 1.4. S or T n = S × ...× S Example 1.5. Gl (n,F) ⊆ F, where F = R or C Example 1.6. E3 = isometries of R (2 connected components) Let the orthogonal group O3 < E3 be the subgroup that fixes the origin, and let the special orthogonal group SO (3) = SO3 < O3 be the orientation-preserving elements of O3. Visualizing SO (3): Let u be a vector of length l in R, correspondi...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1985
ISSN: 0002-9947
DOI: 10.2307/1999680