2024/04/10 by Andrew Douglas, Joe Repka, Douglas, Andrew +1
Mathematics · #17B05 #17B10 #17B20 #17B22 #17B30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2404.07372
openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathfraks \ltimes \mathfrakr be a Levi decomposable Lie algebra, with Levi factor \mathfraks, and radical \mathfrakr. A module V of \mathfraks \ltimes \mathfrakr is cyclic indecomposable if it is indecomposable and the quotient module V /\mathfrakr⋅ V is a simple \mathfraks-module. A Levi decomposable subalgebra of a semisimple Lie algebra is cyclic wide if the restriction of every simple module of the semisimple Lie algebra to the subalgebra is cyclic indecomposable. We establish a condition for a regular Levi decomposable subalgebra of a semisimple Lie algebra to be cyclic wide. Then, in the case of a regular Levi decomposable subalgebra whose radical is an ad-nilpotent subalgebra, we show that the condition is necessary and sufficient for the subalgebra to be cyclic wide. All Lie algebras, and modules in this article are finite-dimensional, and over the complex numbers.