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arXiv · 1111.6128

PostLie algebra structures on the Lie algebra sl(2,C)

Yu Pan·Qing Liu·Chengming Bai·Li Guo
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Abstract

The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and integrable systems. We give a complete classification of PostLie algebra structures on the Lie algebra sl(2,C) up to isomorphism. We first reduce the classification problem to solving an equation of 3 x 3 matrices. To solve the latter problem, we make use of the classification of complex symmetric matrices up to the congruent action of orthogonal groups.

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Yu Pan, Qing Liu, Chengming Bai, Li Guo. 2011-11-26. PostLie algebra structures on the Lie algebra sl(2,C). https://arxiv.org/abs/1111.6128

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