POINCARÉSERIES AND AN APPLICATION TO WEYL ALGEBRAS

doi:10.1016/S0252-9602(11)60246-4

Acta mathematica scientia,Series B ›› 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

WANG Zhi-Hua^1,2, WEI Jun-Chao¹, LI Li-Bin^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)

Let A_n be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over A_n. 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 A_n 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 A_n.

CLC Number:

16D10

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WANG Zhi-Hua, WEI Jun-Chao, LI Li-Bin. POINCARÉSERIES AND AN APPLICATION TO WEYL ALGEBRAS[J].Acta mathematica scientia,Series B, 2011, 31(2): 459-467.

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