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arXiv · 2509.05638

Classification of standard Manin triples in dimension 4+4

Ladislav Hlavatý·Petr Novotný·Ivo Petr
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Abstract

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.

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Ladislav Hlavatý, Petr Novotný, Ivo Petr. 2025-09-06. Classification of standard Manin triples in dimension 4+4. https://doi.org/10.1093/ptep%2Fptaf154

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