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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.02806 |
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| _version_ | 1866910058298736640 |
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| author | Furutani, Kenro Markina, Irina |
| author_facet | Furutani, Kenro Markina, Irina |
| contents | Pseudo $H$-type Lie algebras are a special class of 2-step nilpotent metric Lie algebras, intimately related to Clifford algebras $\Cl_{r,s}$. In this work we propose the classification method for integral orthonormal structures of pseudo $H$-type Lie algebras. We apply this method for the full classification of these structures for $r\in\{1,\ldots,16\}$, $s\in \{0,1\}$ and irreducible Clifford modules. The latter cases form the basis for the further extensions by making use of the Atiyah-Bott periodicity. The existence of integral structures gives rise to the integral discrete uniform subgroups of the pseudo $H$-type Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02806 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Invariant integral structures in pseudo $H$-type Lie algebras: construction and classification Furutani, Kenro Markina, Irina Rings and Algebras Pseudo $H$-type Lie algebras are a special class of 2-step nilpotent metric Lie algebras, intimately related to Clifford algebras $\Cl_{r,s}$. In this work we propose the classification method for integral orthonormal structures of pseudo $H$-type Lie algebras. We apply this method for the full classification of these structures for $r\in\{1,\ldots,16\}$, $s\in \{0,1\}$ and irreducible Clifford modules. The latter cases form the basis for the further extensions by making use of the Atiyah-Bott periodicity. The existence of integral structures gives rise to the integral discrete uniform subgroups of the pseudo $H$-type Lie groups. |
| title | Invariant integral structures in pseudo $H$-type Lie algebras: construction and classification |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2308.02806 |