Abstract
This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples showing substantial differences with the Riemannian situation; for instance, the action of the nilradical of the isometry group does not need to be transitive. For a nilpotent Lie group endowed with a left-invariant pseudo-Riemannian metric, we study conditions for which the subgroup of isometries fixing the identity element equals the subgroup of isometric automorphisms. This set equality holds for pseudo-\(H\)-type Lie groups.
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