数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 459-467.doi: 10.1016/S0252-9602(11)60246-4

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POINCARÉSERIES AND AN APPLICATION TO WEYL ALGEBRAS

王志华1,2|魏俊潮1|李立斌1*   

  1. 1. School of Mathematics, Yangzhou University, Yangzhou 225002, China;
    2. Department of Mathematics, Taizhou College, Nanjing Normal University, Taizhou 225300, China
  • 收稿日期:2008-07-16 修回日期:2009-11-25 出版日期:2011-03-20 发布日期:2011-03-20
  • 基金资助:

    Supported by the National Natural Science Foundation of China (10771182)

POINCARÉSERIES AND AN APPLICATION TO WEYL ALGEBRAS

WANG Zhi-Hua1,2, WEI Jun-Chao1, LI Li-Bin1*   

  1. 1. School of Mathematics, Yangzhou University, Yangzhou 225002, China;
    2. Department of Mathematics, Taizhou College, Nanjing Normal University, Taizhou 225300, China
  • Received:2008-07-16 Revised:2009-11-25 Online:2011-03-20 Published:2011-03-20
  • Supported by:

    Supported by the National Natural Science Foundation of China (10771182)

摘要:

Let An be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over An. By further exploring the relationship between the Poincaré series and the dimension and the multiplicity of M, we are able to prove that the tensor product of two finitely generated modules over An has the multiplicity   equal to the  product of the multiplicities of both modules. It turns out that we can compute the dimensions and the multiplicities of some homogeneous subquotient modules of An.

关键词: Weyl algebra, Poincaré, series, dimension, multiplicity

Abstract:

Let An be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over An. By further exploring the relationship between the Poincaré series and the dimension and the multiplicity of M, we are able to prove that the tensor product of two finitely generated modules over An has the multiplicity   equal to the  product of the multiplicities of both modules. It turns out that we can compute the dimensions and the multiplicities of some homogeneous subquotient modules of An.

中图分类号: 

  • 16D10