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Manoel, Miriam; Oliveira, Leandro N.

Equivariant mappings and invariant sets on Minkowski space. (English) Zbl 1493.22009

Colloq. Math. 167, No. 1, 93-107 (2022).
Authors’ 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.
Reviewer: Benjamin Cahen (Metz)

MSC:

22E43 Structure and representation of the Lorentz group
51B20 Minkowski geometries in nonlinear incidence geometry
13A50 Actions of groups on commutative rings; invariant theory

Keywords:

equivariant mappings; symmetry; Lorentz group; Minkowski space; group representation
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\textit{M. Manoel} and \textit{L. N. Oliveira}, Colloq. Math. 167, No. 1, 93--107 (2022; Zbl 1493.22009)
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