Extended symmetries in supergravity: the semi-simple case

Abstract

The bosonic sector of various supergravity theories reduces to a homogeneous space G/H in three dimensions. The corresponding algebras g are simple for (half-)maximal supergravity, but can be semi-simple for other theories. We extend the existing literature on the Kac-Moody extensions of simple Lie algebras to the semi-simple case. Furthermore, we argue that for N = 2 supergravity the simple algebras have to be augmented with an su(2) factor.