Equivariant mappings and invariant sets on Minkowski space
Volume 167 / 2022
Colloquium Mathematicum 167 (2022), 93-107
MSC: Primary 22E43, 51B20; Secondary 13A50.
DOI: 10.4064/cm7896-10-2020
Published online: 12 May 2021
Abstract
We start a 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 Euclidean space to the Lorentz group acting on 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 those generated by involutions, which is also useful to compute equivariants. Furthermore, general results on invariant subspaces of Minkowski space are presented, with a characterization of invariant lines and planes in the two lowest dimensions.
