# Equivariant mappings and invariant sets on Minkowski space

## TL;DR

This paper systematically studies invariant functions and equivariant mappings on Minkowski space under Lorentz group actions, adapting Euclidean results, and provides algorithms for computing invariants and characterizing invariant subspaces.

## Contribution

It introduces methods to compute generators of invariant functions under Lorentz subgroups and characterizes invariant lines and planes in Minkowski space.

## Key findings

- Algorithm for invariant generator computation
- Characterization of invariant lines and planes
- Extension of Euclidean invariance results to Minkowski space

## Abstract

In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean space to the Lorentz group acting on the Minkowski space. In addition, an algorithm is given to compute generators of the ring of functions that are invariant under an important class of Lorentz subgroups, namely when these are generated by involutions, which is also useful to compute equivariants. Furthermore, general results on invariant subspaces of the Minkowski space are presented, with a characterization of invariant lines and planes in the two lowest dimensions.