Equivariant mappings and invariant sets on Minkowski space

Miriam Manoel, Leandro N. Oliveira Colloquium Mathematicum MSC: Primary 22E43, 51B20; Secondary 13A50. DOI: 10.4064/cm7896-10-2020 Published online: 12 May 2021


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.


  • Miriam ManoelDepartment of Mathematics, ICMC
    University of São Paulo
    13560-970 Caixa Postal 668 São Carlos, Brazil
  • Leandro N. OliveiraDepartment of Mathematics, CCET
    Federal University of São Carlos
    13565-905 Caixa Postal 676 São Carlos, Brazil

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