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arXiv · 1903.00291

Commutative Post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras

Dietrich Burde·Christof Ender
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Abstract

We give an explicit description of commutative post-Lie algebra structures on some classes of nilpotent Lie algebras. For non-metabelian filiform nilpotent Lie algebras and Lie algebras of strictly upper-triangular matrices we show that all CPA-structures are associative and induce an associated Poisson-admissible algebra.

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Dietrich Burde, Christof Ender. 2019-03-01. Commutative Post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras. https://arxiv.org/abs/1903.00291

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