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

Yu Pan, Qing Liu, Chengming Bai, Li Guo

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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. This paper gives a complete classification of PostLie algebra structures on the Lie algebra sl(2,ℂ) up to isomorphism. The classification problem is first reduced to solving an equation of 3 × 3 matrices. Then the latter problem is solved by making use of the classification of complex symmetric matrices up to the congruent action of orthogonal groups.

Original languageEnglish (US)
Pages (from-to)180-197
Number of pages18
JournalElectronic Journal of Linear Algebra
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Classification
  • Lie algebra
  • PostLie algebra
  • Symmetric matrices


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