Hui-Hui An

On flat metric nilpotent Lie algebras

We study flat left-invariant pseudo-Riemannian metrics on nilpotent Lie groups. Associated with a flat metric Lie algebra $(\mathfrak{g},\langle\cdot,\cdot\rangle)$ there is a canonical affine action of the corresponding group on the vector space $\mathfrak{g}$, whose linear part is the Levi-Civita representation $L$....