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 o...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.展开更多
We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior alge...We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra.展开更多
基金supported in part by NSFC #10371036Key Project #2A024 of the Provincial Ministry of Education of Hunan
文摘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.
基金NSFC#10371036,SRFDP#200505042004 the Cultivation Fund of the Key ScientificTechnical Innovation Project #21000115 of the Ministry of Education of China
文摘We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra.
