U (h)-free modules on n -th Schrödinger algebra

AbstractThe n-th Schrödinger algebra schn:=sl2⋉hn is the semi-direct product of the Lie algebra sl2 with the n-th Heisenberg Lie algebra hn. In this paper, we classify the schn-modules (n ≥ 2) that are free of rank 1 when restricted to the Cartan subalgebra (modulo center). Furthermore, the simplicities of these modules are determined.KEYWORDS: n-th Schrödinger algebrassimple modulesU(h)-free modules2020 MATHEMATICS SUBJECT CLASSIFICATION: 17B0517B4017B67 Additional informationFundingThis work is supported by the National Natural Science Foundation of China (Grant No. 11871014 and 11971474) and the Fujian Province Nature Science Foundation (No. 2020J01162).