AdS4 Radius & Cosmological Constant: Is n Relevant?

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The AdS4 radius is related to the cosmological constant by \Lambda =\frac{-3}{b^{2}}.

Is this true in any number of dimensions, or is there a generalised relation depending on number of dimensions n?
 
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In generic dimension d, the cosmological constant is related to AdS radius via \Lambda=-\frac{(d-1)(d-2)}{2\ell^2}.
 

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