Abstract
Following the approach to pseudo-Riemannian symmetric spaces developed in [I. Kath, M. Olbrich, On the structure of pseudo-Riemannian symmetric spaces, arXiv:math.DG/0408249, 2004] we exhibit examples of indefinite hyper-Kähler symmetric spaces with non-abelian holonomy. Moreover, we classify indecomposable hyper-Kähler symmetric spaces whose metric has signature ( 4 , 4 n ) . Such spaces exist if and only if n ∈ { 0 , 1 , 3 } .
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