Commutative post-Lie algebra structures on Kac–Moody algebras

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".

A Zassenhaus conjecture and CPA-structures on simple modular Lie algebras

“…In particular, we have shown that CPA-structures on perfect Lie algebras in characteristic zero are trivial. We also extended this result to some classes of perfect infinitedimensional Lie algebras [16]. The aim of this article is to generalize the result to modular Lie algebras over a field of characteristic p > 0.…”

Crystallographic actions on Lie groups and post-Lie algebra structures

“…However, we could only prove a part of it so far, see [30]. Finally we have determined the CPA-structures on certain infinite-dimensional Lie algebras, e.g., on Kac-Moody algebras [33]. For the infinite-dimensional Witt algebra W in characteristic zero with a set of basis vectors {e i } and Lie brackets [e i , e j ] = (j − i)e i+j we have that all CPA-structures on W are trivial.…”