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I am looking for examples of pseudo-Riemannian symmetric spaces that are not of the type encountered in the standard Riemannian classification, i.e. not flat or with semisimple symmetry group.

As I understand it, for a symmetric space $G/H$ with associated algebras $\mathfrak{g}$ and $\mathfrak{h}$, in these cases the complement of $\mathfrak{h}$ transforms indecomposably under $\mathfrak{h}$. I would like to avoid attempting to construct an example starting from purely this starting point however, and am hoping someone here knows of a nice example. Thanks!

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