2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/204525The 14 Killing vectors of the target space for five-dimensional minimal supergravity reduced to three dimensions are explicitly constructed in terms of the original field variables. These vectors generate the Lie algebra of $G_2$. We also construct a symmetrical $7\times7$ matrix representative of the coset $G_{2(+2)}/((SL(2,R)\times SL(2,R))$ as a function of the same fields.25 pages, typo corrected in Eq. (5.33)General Relativity and Quantum CosmologyHigh Energy Physics - TheoryMathematical Physicstext