  The five dimensional stable de Sitter ground states in N=2 supergravity
obtained by gauging SO(1,1) symmetry of the real symmetric scalar manifold (in
particular a generic Jordan family manifold of the vector multiplets)
simultaneously with a subgroup R_s of the R-symmetry group descend to four
dimensional de Sitter ground states under certain conditions. First, the
holomorphic section in four dimensions has to be chosen carefully by using the
symplectic freedom in four dimensions; and second, a group contraction is
necessary to bring the potential into a desired form. Under these conditions,
stable de Sitter vacua can be obtained in dimensionally reduced theories (from
5D to 4D) if the semi-direct product of SO(1,1) with R^(1,1) together with a
simultaneous R_s is gauged. We review the stable de Sitter vacua in four
dimensions found in earlier literature for N=2 Yang-Mills Einstein supergravity
with SO(2,1) x R_s gauge group in a symplectic basis that comes naturally after
dimensional reduction. Although this particular gauge group does not descend
directly from five dimensions, we show that, its contraction does. Hence, two
different theories overlap in certain limits. Examples of stable de Sitter
vacua are given for the cases: (i) R_s=U(1)_R, (ii) R_s=SU(2)_R, (iii) N=2
Yang-Mills/Einstein Supergravity theory coupled to a universal hypermultiplet.
We conclude with a discussion regarding the extension of our results to
supergravity theories with more general homogeneous scalar manifolds.
