N=8 BPS Black Holes with 1/2 or 1/4 Supersymmetry and Solvable Lie Algebra Decomposition

In the context of N = 8 supergravity we construct the general form of BPS 0-branes that preserve either 12 or 14 of the original supersymmetry. We show how solutions are related to suitable decompositions of the 70-dimensional solvable Lie algebra that describes the scalar field sector. We compare our new results to those obtained in a previous paper for the case of 18 supersymmetry preserving black holes. Each of the three cases is based on a different solvable Lie algebra decomposition and leads to a different structure of the scalar field evolution and of their fixed values at the horizon of the black hole.