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Indecomposable representations of the Lie algebra of derivations for d-torus

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Abstract

Let DerA be the Lie algebra of derivations of the d-torus \( A = \mathbb{C}[t_1^{ \pm 1} ,...,t_d^{ \pm 1} ] \). By applying Shen-Larsson’s functors we get a class of indecomposable DerA-modules from finite-dimensional indecomposable gl d -modules. We also give a complete description of the submodules of these indecomposable DerA-modules. Our results generalize those obtained by Rao.

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Authors and Affiliations

  1. Department of Mathematics, Xiamen University, Xiamen, 361005, China

    HaiFeng Lian & ShaoBin Tan

  2. Department of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou, 350002, China

    HaiFeng Lian

  3. Department of Mathematics, Xiangtan University, Xiangtan, 411105, China

    Bo Zeng

Authors
  1. HaiFeng Lian
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  2. ShaoBin Tan
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  3. Bo Zeng
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Correspondence to ShaoBin Tan.

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Lian, H., Tan, S. & Zeng, B. Indecomposable representations of the Lie algebra of derivations for d-torus. Sci. China Math. 53, 305–314 (2010). https://doi.org/10.1007/s11425-009-0034-6

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  • DOI: https://doi.org/10.1007/s11425-009-0034-6

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