Generalization of extended Lie algebras by expansions of extended de Sitter algebra, in four-dimensions

Abstract: Four-dimensional extended: Poincar\'e, AdS-Lorentz and Maxwell algebras, are obtained by expanding an extension of de Sitter or conformal algebra, SO(4,1) or SO(3,2). The procedure can be generalized to obtain a new family of extended $\mathcal{C}_k^{E}$ and its flat limit, the extended $\mathcal{B}_k^{E}$ algebras. The extended $\mathcal{C}_k$ and $\mathcal{B}_k$ algebras have been introduced in the literature recently.The extended Poincar\'e algebra is also obtained as an In\"on\"u-Wigner contraction of extended de Sitter algebra.