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arXiv · 1802.06539

Existence of cocompact lattices in Lie groups with a bi-invariant metric of index 2

Ines Kath
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Abstract

We study the existence of cocompact lattices in Lie groups with bi-invariant metric of signature $(2,n-2)$. We assume in addition that the Lie groups under consideration are simply-connected, indecomposable and solvable. Then their centre is one- or two-dimensional. In both cases, a parametrisation of the set of such Lie groups is known. We give a necessary and sufficient condition for the existence of a lattice in terms of these parameters. For groups with one-dimensional centre this problem is related to Salem numbers.

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Ines Kath. 2018-02-19. Existence of cocompact lattices in Lie groups with a bi-invariant metric of index 2. https://arxiv.org/abs/1802.06539

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