Extension of the Poincar\'e group with half-integer spin generators: hypergravity and beyond

An extension of the Poincar\'e group with half-integer spin generators is explicitly constructed. We start discussing the case of three spacetime dimensions, and as an application, it is shown that hypergravity can be formulated so as to incorporate this structure as its local gauge symmetry. Since the algebra admits a nontrivial Casimir operator, the theory can be described in terms of gauge fields associated to the extension of the Poincar\'e group with a Chern-Simons action. The algebra is also shown to admit an infinite-dimensional non-linear extension, that in the case of fermionic spin-$3/2$ generators, corresponds to a subset of a contraction of two copies of WB$_2$. Finally, we show how the Poincar\'e group can be extended with half-integer spin generators for $d\geq3$ dimensions.