Multiplicity-one representations of divergence-free Lie algebras
In this work, the author considers a special class of \(S\)-modules, where \(S\) is a graded generalized divergence-free Lie algebra according to the Đokovic-Zhao approach [\textit{D. Z. Đoković} and \textit{K. Zhao}, ``Generalized Cartan type \(S\) Lie algebras in characteristic zero'', J. Algebra 193, No. 1, 144--179 (1997; Zbl 0978.17015)]. The main result of the paper is the classification of indecomposable graded \(S\)-modules with the property that their homogeneous components have dimension \(0\) or \(1\). The five classes of indecomposable modules over a generalized Witt algebra with 1-dimensional weight spaces and their restriction to the \(S\) algebras play an central role in this classification [\textit{K. Zhao}, ``Weight modules over generalized Witt algebras with 1-dimensional weight spaces'', Forum Math. 16, No. 5, 725--748 (2004; Zbl 1069.17002)].
scientific article; zbMATH DE number 6055209
scientific article