Compatible root graded anti-pre-Lie algebraic structures on finite-dimensional complex simple Lie algebras
arXiv:2503.15241
Abstract
We investigate the compatible root graded anti-pre-Lie algebraic structures on any finite-dimensional complex simple Lie algebra by the representation theory of ${\rm sl_2(\C)}$. We show that there does not exist a compatible root graded anti-pre-Lie algebraic structure on a finite-dimensional complex simple Lie algebra except ${\rm sl_2(\C)}$, whereas there is exactly one compatible root graded anti-pre-Lie algebraic structure on ${\rm sl_2(\C)}$.
18 pages