Equivariant mappings and invariant sets on Minkowski space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866913757954834432 |
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| author | Manoel, Miram de Oliveira, Leandro Nery |
| author_facet | Manoel, Miram de Oliveira, Leandro Nery |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1904_09001 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Equivariant mappings and invariant sets on Minkowski space Manoel, Miram de Oliveira, Leandro Nery Representation Theory 22E43, 51B20, 13A50 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. |
| title | Equivariant mappings and invariant sets on Minkowski space |
| topic | Representation Theory 22E43, 51B20, 13A50 |
| url | https://arxiv.org/abs/1904.09001 |