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Compatible root graded anti-pre-Lie algebraic structures on finite-dimensional complex simple Lie algebras (2503.15241v1)
Published 19 Mar 2025 in math.QA, math.RA, and math.RT
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 ${\rm sl_2(\C)}$.