# Conformal numbers

## TL;DR

This paper explores the structure of conformal compactifications within hypercomplex projective spaces, using bicomplex matrices to analyze geometries relevant to physics such as Minkowski and Anti-de Sitter spaces.

## Contribution

It introduces a novel framework for expressing conformal geometries in hypercomplex projective spaces via bicomplex Vahlen matrices and their structural components.

## Key findings

- Representation of conformal geometries using bicomplex matrices
- Hierarchical relation between projective spaces in hypercomplex settings
- Application to physics-related geometries like Minkowski and Anti-de Sitter spaces

## Abstract

The conformal compactification is considered in a hierarchy of hypercomplex projective spaces with relevance in physics including Minkowski and Anti-de Sitter space. The geometries are expressed in terms of bicomplex Vahlen matrices and further broken down into their structural components. The relation between two subsequent projective spaces is displayed in terms of the complex unit and three additional hypercomplex numbers.