Higher-dimensional gravity invariant under the AdS group

A higher-dimensional gravity invariant both under local Lorentz rotations and under local anti-de Sitter boosts is constructed. It is shown that such a construction is possible both when odd dimensions and when even dimensions are considered. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli [Class. Quantum Grav. 17 (2000) 4451].