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arXiv · 1705.05993

3-Lie bialgebras and 3-Lie classical Yang-Baxter equations in low dimensions

Chengyu Du·Chengming Bai·Li Guo
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Abstract

In this paper, we give some low-dimensional examples of local cocycle 3-Lie bialgebras and double construction 3-Lie bialgebras which were introduced in the study of the classical Yang-Baxter equation and Manin triples for 3-Lie algebras. We give an explicit and practical formula to compute the skew-symmetric solutions of the 3-Lie classical Yang-Baxter equation (CYBE). As an illustration, we obtain all skew-symmetric solutions of the 3-Lie CYBE in complex 3-Lie algebras of dimension 3 and 4 and then the induced local cocycle 3-Lie bialgebras. On the other hand, we classify the double construction 3-Lie bialgebras for complex 3-Lie algebras in dimensions 3 and 4 and then give the corresponding 8-dimensional pseudo-metric 3-Lie algebras.

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BibTeXRIS

Chengyu Du, Chengming Bai, Li Guo. 2017-05-17. 3-Lie bialgebras and 3-Lie classical Yang-Baxter equations in low dimensions. https://doi.org/10.1080/03081087.2017.1366413

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