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On the Category of Koszul Modules of Complexity One of an Exterior Algebra

On the Category of Koszul Modules of Complexity One of an Exterior Algebra
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摘要 In this paper, we prove that there is a natural equivalence between the category F1(x) of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables. In this paper, we prove that there is a natural equivalence between the category F1(x) of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第3期849-854,共6页 数学学报(英文版)
基金 supported in part by NSFC #10371036 Key Project #2A024 of the Provincial Ministry of Education of Hunan
关键词 exterior algebra Koszul module COMPLEXITY exterior algebra, Koszul module, complexity
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