Timeline for Subgroups of $E(n) = \mathbb{R}^n \rtimes O(n)$ with trivial orbit space
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2014 at 5:10 | vote | accept | David Ong | ||
| Feb 4, 2014 at 22:33 | comment | added | Claudio Gorodski | @qswang: I am no expert on this matter, but a quick search in the literature seems to indicate that the claim of Scheuneman to have proved the Auslander conjecture in full was incorrect, so indeed Fried found a counterexample, namely, a simply-transitivve affine action of a 3-step nilpotent 4-dimensional connected and simply-connected Lie group in which the only element acting as a pure translation is the identity. Nevertheless, the conjecture has been shown to hold for some classes of groups, for instance in dimension $3$ (by Fried and Goldman). | |
| Feb 4, 2014 at 12:45 | comment | added | David Ong | The conjecture was came from " Simply transitive groups of affine motions" of L. Auslander. | |
| Feb 4, 2014 at 12:40 | comment | added | David Ong | $\mathfrak g=\{\tau_v+\varphi(v):v\in V$ Is this implies G consists all pure translations in U which is not empty? In the affine motion case,the conjecture that "any nilpotent simply transitive group of affine motions must contain a one-parameter group of pure translations in its centre" was verified by JOHN SCHEUNEMAN in "TRANSLATIONS IN CERTAIN GROUPS OF AFFINE MOTIONS",and an counterexample by D. Fried occured in "Distality, completeness and affine structures" Its confusing. Who is right? Is there any reference of simply transitive group of Rigid Motion rather than affine motion? | |
| Feb 1, 2014 at 16:48 | history | edited | Claudio Gorodski | CC BY-SA 3.0 |
Corrected typo.
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| Feb 1, 2014 at 16:38 | history | undeleted | Claudio Gorodski | ||
| Feb 1, 2014 at 16:38 | history | edited | Claudio Gorodski | CC BY-SA 3.0 |
added 2322 characters in body
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| Feb 1, 2014 at 16:16 | history | deleted | Claudio Gorodski | via Vote | |
| Feb 1, 2014 at 15:56 | history | answered | Claudio Gorodski | CC BY-SA 3.0 |