Commutative post-Lie algebra structures on Lie algebras

By Dietrich Burde, Wolfgang Alexander Moens. 2015

47 citations recorded by the source corpus.

We show that any CPA-structure (commutative post-Lie algebra structure) on a perfect Lie algebra is trivial. Furthermore we give a general decomposition of inner CPA-structures, and classify all CPA-structures on parabolic subalgebras of simple Lie algebras.

View Paper: https://www.semanticscholar.org/paper/2622490fd481656fdd48eac7b43c61967564fc7e

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1. Li Guo
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5. Xiaomin Tang
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Citations in the corpus

• Post-groups, (Lie-)Butcher groups and the Yang–Baxter equation (2023, methodology): “Lax pairs, classifications of post-Lie algebras on certain Lie algebras, Poincaré-Birkhoff-Witt theorems, factorization theorems and regularity structures in singular stochastic partial differential equations [2, 8, 5, 20, 23].”
• Biderivations, linear commuting maps and commutative post-Lie algebra structures on W-algebras (2017, background): “Recently, many authors study some post-Lie algebras and post-Lie algebra structures [8, 9, 25, 26, 30].”