I'm trying to derive the lie algebra for Anti desitter space in 3+1 I know it's O(4,1) and I think I understand that but I'm taking different approach. I tried to derive the conformal killing vectors by solving Killing's equation, but when I got my solution the conformal factor vanished .(adsbygoogle = window.adsbygoogle || []).push({});

The solution I got for the Killing vectors is:

[tex]

\xi _t = - r\sqrt {1 + \left( {r/R} \right)^2 } \sin \theta \left( {A\sin \phi \cos \left( {t/R} \right) - B\cos \phi \cos (t/R) + C\sin \phi \sin (t/R)} \right)

[/tex]

[tex]

\xi _r = \frac{R}

{{\sqrt {1 + \left( {r/R} \right)^2 } }}\sin \theta \left( {A\sin \phi \sin (t/R) - B\cos \phi \sin (t/R) - C\sin \phi \cos (t/R) + D\cos \phi \cos \left( {t/R} \right)} \right)

[/tex]

[tex]

\xi _\theta = rR\sqrt {1 + \left( {r/R} \right)^2 } \cos \theta \left( {A\sin \phi \sin \left( {t/R} \right) - B\cos \phi \sin \left( {t/R} \right) - C\sin \phi \cos \left( {t/R} \right) + D\cos \phi \cos \left( {t/R} \right)} \right)

[/tex]

[tex]

\xi _\phi = rR\sqrt {1 + \left( {r/R} \right)^2 } \sin \theta \left( {A\cos \phi \sin \left( {t/R} \right) + B\sin \phi \sin \left( {t/R} \right) - C\cos \phi \cos \left( {t/R} \right) - D\sin \phi \cos \left( {t/R} \right)} \right)

[/tex]

These do satisfy the killing equation, but I feel like i"m missing something.

they only has 4 unknowns A, B, C, D not 10 like SO(1,4), also I don't understand how Teitelbohm and Henneaux got their lie algebra in their paper asymptotically anti de sitter spaces.

Any help will be much appreciated.

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# Killing vectors for Anti desitter space in 3+1

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