Timeline for Action on a compact group
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2011 at 16:53 | comment | added | algori | Drike -- one reference is Hofmann-Morris, The structure of compact groups, De Gruyter Studies in Mathematics 25, in particular chapter 8, the structure theory of abelian compact groups. Every such group has a totally disconnected normal subgroup with quotient a torus (proposition 8.15). The structure of totally disconnected groups is given in ibid., Proposition 8.8. | |
| Nov 4, 2011 at 12:42 | vote | accept | Drike | ||
| Nov 4, 2011 at 6:33 | comment | added | Drike | Many thanks for your answer. Would you have any references where I could check the details (and learn more about Aut(C) when C is a compact group) ? Also, do you think there are essential differences on the structure of such a compact group C depending on whever the set of orbits is countable or uncountable ? Can the set of orbits be of size aleph_1 ? | |
| Nov 4, 2011 at 6:20 | vote | accept | Drike | ||
| Nov 4, 2011 at 6:31 | |||||
| Nov 3, 2011 at 21:35 | comment | added | Alain Valette | Still another example: the Cantor group $C=\{0,1\}^\mathbb{N}$; here there are countably many orbits under $Aut(C)$. | |
| Nov 3, 2011 at 18:18 | comment | added | Alain Valette | One more example: for $G=\mathbb{T}^n$ (the $n$-dimensional torus), $Aut(G)=GL_n(\mathbb{Z})$, so there are uncountably many orbits. | |
| Nov 3, 2011 at 11:50 | history | edited | algori | CC BY-SA 3.0 |
added 449 characters in body; deleted 7 characters in body
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| Nov 3, 2011 at 11:33 | history | answered | algori | CC BY-SA 3.0 |