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

2019/03/01 by Burde, Dietrich, Ender, Christof
#17B30 #17D25 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1903.00291

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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• Commutative post-Lie algebra structures and linear equations for nilpotent Lie algebras
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• Post-Lie algebra structures for nilpotent Lie algebras
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