Commutative post-Lie algebra structures on Kac--Moody algebras
arXiv:1805.04267 · doi:10.1080/00927872.2019.1612426
Abstract
We determine commutative post-Lie algebra structures on some infinite-dimensional Lie algebras. We show that all commutative post-Lie algebra structures on loop algebras are trivial. This extends the results for finite-dimensional perfect Lie algebras. Furthermore we show that all commutative post-Lie algebra structures on affine Kac--Moody Lie algebras are "almost trivial".
8 pages; to appear in Comm. Algebra; v2: minor changes