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Expansions of Lie algebras are the opposite process of contractions. Startingfrom a Lie algebra, the expansion process goes to another one, non-isomorphicand less abelian. We propose an expansion method based in the Casimirinvariants of the initial and expanded algebras and where the free parametersinvolved in the expansion are the curvatures of their associated homogeneousspaces. This method is applied for expansions within the family of Lie algebrasof 3d spaces and (2+1)d kinematical algebras. We show that these expansions areclassed in two types. The first type makes different from zero the curvature ofspace or space-time (i.e., it introduces a space or universe radius), while theother has a similar interpretation for the curvature of the space ofworldlines, which is non-positive and equal to $-1/c^2$ in the kinematicalalgebras. We get expansions which go from Galilei to either Newton--Hooke orPoincar\'e algebras, and from these ones to de Sitter algebras, as well as someother examples.Comment: 15 pages, LaTe

2 + 1 kinematical expansions: from Galilei to de Sitter algebras