Nested Affine Buildings and Their Group Decompositions
Group Theory
2025-12-23 v1 Number Theory
Abstract
In this paper, we construct a higher dimensional generalization of affine buildings and introduce a new structure, which we call Babel buildings. These buildings are non-connected, non-convex metric spaces of non-positive curvature. Despite their non-standard properties, Babel buildings provide an effective framework for studying the structure of groups acting on them. We analyze the metric and nesting structures of Babel buildings and derive key results regarding the group actions consistent with this new framework.
Cite
@article{arxiv.2512.18628,
title = {Nested Affine Buildings and Their Group Decompositions},
author = {Masaoki Mori},
journal= {arXiv preprint arXiv:2512.18628},
year = {2025}
}