so(D - 1, 1) ⊕ so (D - 1, 2) algebras and gravity

It is shown that using a specific semigroup, the S-expansion of the AdS Lie algebra leads to a generalization of the so (D - 1, 1) circle plus so(D - 1, 2) algebras, which are called generalized AdS-Lorentz algebras. The generalized Inonu-Wigner contraction of the generalized AdS-Lorentz algebras provides the so-called B-m algebras. The B-4 algebra corresponds to the so-called Maxwell algebra. The B-m algebras can be also obtained by S-expansion of the AdS Lie algebra when we use a semigroup endowed with a multiplication law different from the law of multiplication of semigroup above. Chern-Simons as well as Born-Infeld gravities actions, which in a certain limit contain the Einstein-Hilbert Lagrangian with a cosmological term, are also constructed. (C) 2013 Elsevier B.V. All rights reserved.