Groups and Cantor sets

TL;DR

This paper explores p-adic analogues of a well-studied nilpotent Lie group formed by upper-triangular matrices with ones on the diagonal, focusing on their geometric and dilation properties.

Contribution

It introduces p-adic versions of the classical nilpotent Lie group and investigates their geometric structures and dilation behaviors.

Findings

p-adic groups exhibit similar dilation structures to real cases

New geometric properties are identified in the p-adic setting

Connections between p-adic and real nilpotent groups are established

Abstract

It is well known that n x n upper-triangular real matrices with 1's on the diagonal form a nilpotent Lie group with an interesting family of non-isotropic dilations and corresponding geometry, as in [9]. Here we look at p-adic versions of this, and related matters.