We show that the so-called semi-simple extended Poincaré (SSEP) algebra in D dimensions can be obtained from the anti-de Sitter algebra so (D − 1, 2) by means of the S-expansion procedure with an appropriate semigroup S. A general prescription is given for computing Casimir operators for S-expanded algebras, and the method is exemplified for the SSEP algebra. The S-expansion method also allows us to extract the corresponding invariant tensor for the SSEP algebra, which is a key ingredient in the construction of a generalized action for Chern-Simons gravity in 2 + 1

The coupling of spin-3 gauge fields to three-dimensional Maxwell and AdS-Lorentz gravity theories is presented. After showing how the usual spin-3 extensions of the AdS and the Poincaré algebras in three dimensions can be obtained as expansions of sl (3, R) algebra, the procedure is generalized so as to define new higher-spin symmetries. Remarkably, the spin-3 extension of the Maxwell symmetry allows one to introduce a novel gravity model coupled to higherspin topological matter with vanishing cosmological constant, which in turn corresponds to a flat limit of the AdS-Lorentz case. We extend our results to define two different families of higher-spin extensions of three-dimensional Einstein

We present a generalization of the standard Inönü-Wigner contraction by rescaling not only the generators of a Lie superalgebra but also the arbitrary constants appearing in the components of the invariant tensor. The procedure presented here allows one to obtain explicitly the Chern-Simons supergravity action of a contracted superalgebra. In particular we show that the Poincaré limit can be performed to a D = 2 + 1 ( p, q) AdS Chern-Simons supergravity in presence of the exotic form. We also construct a new three-dimensional (2, 0) Maxwell Chern-Simons supergravity theory as a particular limit of (2, 0) AdS-Lorentz supergravity theory. The generalization for N = p + q gravitinos is also considered.

We present the construction of the D = 3 Chern-Simons supergravity action without cosmological constant from the minimal Maxwell superalgebra sM3. This superalgebra contains two Majorana fermionic charges and can be obtained from the osp (2|1) ⊗ sp (2) superalgebra using the abelian semigroup expansion procedure. The components of the Maxwell invariant tensor are explicitly derived.

A new approach for obtaining the three-dimensional Chern-Simons supergravity for the Poincaré algebra is presented. The N -extended Poincaré supergravity is obtained by expanding the super Lorentz theory. We extend our procedure to their respective asymptotic symmetries and show that the N = (1, 2, 4) super-BMS 3 appear as expansions of one Virasoro superalgebra. Interestingly, the N -extended super-BMS 3 obtained here are not only centrally extended but also endowed with internal symmetry. We also show that the N -extended super Poincaré algebras with both central and automorphism generators are finite subalgebras.