Is the action of $SO(1,2)$ in null cone proper?












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It is known that the action of the group $SO(1,2)$ on the null-cone inside the $3$-dimensional Minkowski space is free and transitive. However, is the action also proper?










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    $begingroup$
    In a free group action, all the orbits are essentially a copy of the group itself. But the null-cone is 2D whereas the Lie group SO(1,2) is 3D, so how can the action be free?
    $endgroup$
    – arctic tern
    Dec 15 '18 at 3:09
















0












$begingroup$


It is known that the action of the group $SO(1,2)$ on the null-cone inside the $3$-dimensional Minkowski space is free and transitive. However, is the action also proper?










share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    In a free group action, all the orbits are essentially a copy of the group itself. But the null-cone is 2D whereas the Lie group SO(1,2) is 3D, so how can the action be free?
    $endgroup$
    – arctic tern
    Dec 15 '18 at 3:09














0












0








0





$begingroup$


It is known that the action of the group $SO(1,2)$ on the null-cone inside the $3$-dimensional Minkowski space is free and transitive. However, is the action also proper?










share|cite|improve this question











$endgroup$




It is known that the action of the group $SO(1,2)$ on the null-cone inside the $3$-dimensional Minkowski space is free and transitive. However, is the action also proper?







lie-groups group-actions






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 11 '18 at 6:00









user1101010

9011830




9011830










asked Dec 11 '18 at 5:33









VarunVarun

11




11








  • 1




    $begingroup$
    In a free group action, all the orbits are essentially a copy of the group itself. But the null-cone is 2D whereas the Lie group SO(1,2) is 3D, so how can the action be free?
    $endgroup$
    – arctic tern
    Dec 15 '18 at 3:09














  • 1




    $begingroup$
    In a free group action, all the orbits are essentially a copy of the group itself. But the null-cone is 2D whereas the Lie group SO(1,2) is 3D, so how can the action be free?
    $endgroup$
    – arctic tern
    Dec 15 '18 at 3:09








1




1




$begingroup$
In a free group action, all the orbits are essentially a copy of the group itself. But the null-cone is 2D whereas the Lie group SO(1,2) is 3D, so how can the action be free?
$endgroup$
– arctic tern
Dec 15 '18 at 3:09




$begingroup$
In a free group action, all the orbits are essentially a copy of the group itself. But the null-cone is 2D whereas the Lie group SO(1,2) is 3D, so how can the action be free?
$endgroup$
– arctic tern
Dec 15 '18 at 3:09










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