Compatible root graded anti-pre-Lie algebraic structures on finite-dimensional complex simple Lie algebras

2025/03/19 by Bai, Chengming, Gao, Dongfang
#17B10 #17B65 #17B66 #17B68 #17B70 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/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 sl₂(\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 sl₂(\C), whereas there is exactly one compatible root graded anti-pre-Lie algebraic structure on \rm sl₂(\C).

Related

• Compatible anti-pre-Lie algebras
• Constructing Graded Lie Algebras
• Graded anti-pre-Lie algebraic structures on Witt and Virasoro algebras
• Lie algebras whose derivation algebras are simple
• Lie antialgebras: premices