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Postlie algebra structures on the Lie algebra $SL\left(2,Ca\right)$. (English) Zbl 06100977
Summary: 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 $sl\left(2,C\right)$ up to isomorphism.
##### MSC:
 17A30 Nonassociative algebras satisfying other identities 17A42 Other $n$-ary compositions $\left(n\ge 3\right)$ 17B60 Lie (super)algebras associated with other structures 18D50 Operads
##### Keywords:
Lie algebra; postlie algebra; symmetric matrices