The Heisenberg group acts on a strictly convex domain

TL;DR

This paper presents the first example of a unipotent group that is not virtually abelian and still preserves a strictly convex domain, expanding understanding of group actions on convex geometries.

Contribution

It provides the first known example of a non-virtually abelian unipotent group acting on a strictly convex domain, challenging previous assumptions.

Findings

Identifies a unipotent group that preserves a strictly convex domain

Demonstrates the group's non-virtually abelian nature

Expands the class of groups known to act on convex domains

Abstract

This paper gives the first example of a unipotent group that is not virtually abelian and preserves a strictly convex domain.