Dra. Rodríguez-Durán, Evelyn

In this work, we apply the semigroup expansion method of Lie algebras to construct novel and known three-dimensional hyper-gravity theories. We show that the expansion procedure considered here yields a consistent way of coupling different three-dimensional Chern-Simons gravity theories with massless spin- 5/2 gauge fields. First, by expanding the osp (1|4) superalgebra with a particular semigroup a generalized hyper-Poincaré algebra is found. Interestingly, the hyper-Poincaré and hyper-Maxwell algebras appear as subalgebras of this generalized hyper-symmetry algebra. Then, we show that the generalized hyper-Poincaré CS gravity action can be written as a sum of diverse hyper-gravity CS Lagrangians. We extend our study to a generalized hyper-AdS gravity theory by considering a different semigroup. Both generalized hyperalgebras are then found to be related through an Inönü-Wigner contraction which can be seen as a generalization of the existing vanishing cosmological constant limit between the hyper-AdS and hyper-Poincaré gravity theories.

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 higher-spin 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 gravity.

By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 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 Bk, Ck and Dk 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.