By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms 3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called B k , C k and D k algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

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

In this paper we show that some 3-dimensional isometry algebras, specifically those of type I, II, III and V ( according Bianchi's classification), can be obtained as expansions of the isometries in 2 dimensions. It is shown that in general more than one semigroup will lead to the same result. It is impossible to obtain the algebras of type IV, VI-IX as an expansion from the isometry algebras in 2 dimensions. This means that the first set of algebras has properties that can be obtained from isometries in 2 dimensions while the second set has properties that are in some sense intrinsic in 3 dimensions. All the results are checked with computer programs. This procedure can be generalized to higher dimensions, which could be useful for diverse physical applications.

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.

In this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-BM S 3 , the superconformal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. The new superalgebras obtained are supersymmetric extensions of the asymptotic algebras of the Maxwell and the so(2, 2) ⊕ so(2, 1) gravity theories. We extend our results to the N = 2 and N = 4 cases and find that R-symmetry generators are required. We also show that the new infinite-dimensional structures are related through a flat limit ℓ → ∞. Conclusions 316 Acknowledgment 32