Doubly extended Lie groups - curvature, holonomy and parallel spinors

In the present paper we study the geometry of doubly extended Lie groups with their natural biinvariant metric. We describe the curvature, the holonomy and the space of parallel spinors. This is completely done for all simply connected groups with biinvariant metric of Lorentzian signature (1, n-1), of signature (2, n-2) and of signature (p, q), where p + q less than or equal to 6. Furthermore, some special series with higher signature are discussed. (C) 2003 Elsevier B.V. All rights reserved.