On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915722817437696 |
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| author | Filimoshina, E. R. Shirokov, D. S. |
| author_facet | Filimoshina, E. R. Shirokov, D. S. |
| contents | This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that these Lie groups can be equivalently defined using norm functions of multivectors applied in the theory of spin groups. We also study the corresponding Lie algebras. Some of these Lie groups and algebras are closely related to Heisenberg Lie groups and algebras. The introduced groups are interesting for various applications in physics and computer science, in particular, for constructing equivariant neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07191 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras Filimoshina, E. R. Shirokov, D. S. Rings and Algebras Machine Learning Mathematical Physics 15A66, 11E88 This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that these Lie groups can be equivalently defined using norm functions of multivectors applied in the theory of spin groups. We also study the corresponding Lie algebras. Some of these Lie groups and algebras are closely related to Heisenberg Lie groups and algebras. The introduced groups are interesting for various applications in physics and computer science, in particular, for constructing equivariant neural networks. |
| title | On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras |
| topic | Rings and Algebras Machine Learning Mathematical Physics 15A66, 11E88 |
| url | https://arxiv.org/abs/2601.07191 |