Classification of Lie algebras of specific type in complexified Clifford algebras
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866915074122186752 |
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| author | Shirokov, D. S. |
| author_facet | Shirokov, D. S. |
| contents | We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical matrix Lie algebras in the cases of arbitrary dimension and signature. We present sixteen Lie groups: one Lie group for each Lie algebra associated with this Lie group. We study connection between these groups and spin groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1704_03713 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Classification of Lie algebras of specific type in complexified Clifford algebras Shirokov, D. S. Mathematical Physics 15A66, 22E60 We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical matrix Lie algebras in the cases of arbitrary dimension and signature. We present sixteen Lie groups: one Lie group for each Lie algebra associated with this Lie group. We study connection between these groups and spin groups. |
| title | Classification of Lie algebras of specific type in complexified Clifford algebras |
| topic | Mathematical Physics 15A66, 22E60 |
| url | https://arxiv.org/abs/1704.03713 |