  In this work, we classify all extended and generalized kinematical Lie
algebras that can be obtained by expanding the $\mathfrak{so}\left(2,2\right)$
algebra. We show that the Lie algebra expansion method based on semigroups
reproduces not only the original kinematical algebras but also a family of non-
and ultra-relativistic algebras. Remarkably, the extended kinematical algebras
obtained as sequential expansions of the AdS algebra are characterized by a
non-degenerate bilinear invariant form, ensuring the construction of a
well-defined Chern-Simons gravity action in three spacetime dimensions.
Contrary to the contraction process, the degeneracy of the non-Lorentzian
theories is avoided without extending the relativistic algebra but considering
a bigger semigroup. Using the properties of the expansion procedure, we show
that our construction also applies at the level of the Chern-Simons action.
