Indecomposable modules of 2-step solvable Lie algebras in arbitrary characteristic

2014/08/09 by Cagliero, Leandro, Szechtman, Fernando
#17B10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1408.2166

Abstract

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

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