Lattices in the four-dimensional split oscillator group

2021/03/26 by Galiay, Blandine, Kath, Ines
#22E40 #53C50 #57S30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.14618

Abstract

Besides the oscillator group, there is another four-dimensional non-abelian solvable Lie group that admits a bi-invariant pseudo-Riemannian metric. It is called split oscillator group (sometimes also hyperbolic oscillator group or Boidol's group). We parametrise the set of lattices in this group and develop a method to classify these lattices up automorphisms of the ambient group. We show that their commensurability classes are in bijection with the set of real quadratic fields.

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