Indecomposable Modules of 2-step Solvable Lie Algebras in Arbitrary Characteristic

Abstract

Let F be an algebraically closed field and consider the Lie algebra 𝔤 = ⟨ x ⟩ ⋉ 𝔞, where ad x acts diagonalizably on the abelian Lie algebra 𝔞. Refer to a 𝔤-module as admissible if [𝔤, 𝔤] acts via nilpotent operators on it, which is automatic if chr(F) = 0. In this article, we classify all indecomposable 𝔤-modules U which are admissible as well as uniserial, in the sense that U has a unique composition series.

Key Words:

• Indecomposable module
• Lie algebra
• Uniserial module

2010 Mathematics Subject Classification:

• Primary: 17B10
• 17B30
• 17B50

Notes

Communicated by A. Elduque.