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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.05638 |
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| _version_ | 1866918223456239616 |
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| author | Hlavatý, Ladislav Novotný, Petr Petr, Ivo |
| author_facet | Hlavatý, Ladislav Novotný, Petr Petr, Ivo |
| contents | Four- and six-dimensional Drinfeld doubles were classified in the past in terms of Manin triples. We provide an important step towards the classification of eight-dimensional Drinfeld doubles by presenting an extensive list of Manin triples formed by pairs of four-dimensional Lie algebras. Due to the high complexity of the classification we focus on Manin triples formed by algebras in a certain standard form. The list contains 188 non-isomorphic Manin triples plus their duals.
To apply the results, we construct several four-dimensional WZW models on non-semisimple Lie groups. Some of the WZW models are known from the literature, but new cases are presented as well. As a consequence of the construction method, the WZW models are Poisson--Lie dualizable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of standard Manin triples in dimension 4+4 Hlavatý, Ladislav Novotný, Petr Petr, Ivo High Energy Physics - Theory Four- and six-dimensional Drinfeld doubles were classified in the past in terms of Manin triples. We provide an important step towards the classification of eight-dimensional Drinfeld doubles by presenting an extensive list of Manin triples formed by pairs of four-dimensional Lie algebras. Due to the high complexity of the classification we focus on Manin triples formed by algebras in a certain standard form. The list contains 188 non-isomorphic Manin triples plus their duals. To apply the results, we construct several four-dimensional WZW models on non-semisimple Lie groups. Some of the WZW models are known from the literature, but new cases are presented as well. As a consequence of the construction method, the WZW models are Poisson--Lie dualizable. |
| title | Classification of standard Manin triples in dimension 4+4 |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.05638 |