Maximally $\cal{N}$-extended super-BMS$_3$ algebras and Generalized 3D Gravity Solutions

We consider the maximal $\cal{N}-$extended supergravity theory in 3 dimensions with fermionic generators transforming under real but non necessarily irreducible representations of the internal algebra. We obtain the symmetry algebra at null infinity preserving boundary conditions of asymptotically flat solutions, i.e. the maximal $\cal{N}-$extended super-BMS$_3$ algebra, which possesses non-linear correction in the anti-commutators of supercharges. We present the supersymmetric energy bound and derive the explicit form of the asymptotic Killing spinors. We also find the most generic circular symmetric ground state of the theory, which corresponds to a non-supersymmetric cosmological solutions and derive their entropy.