Abstract
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 Λ = ∧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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ringel, C. M.: Tame algebra and integral quadratic forms, Lecture Note in Mathematics no.1099, Springer Verlag, Berlin, 1994
Guo, J. Y., Wu, Q. X., Wan, Q. H.: On the tubes of exterior algebras, preprint
Eisenbud, D.: Periodic resolutions over exterior algebras. Special issue in celebration of Claudio Procesi’s 60th birthday. J. Algebra, 258(1), 348–361 (2002)
Bernstein, I. N., Gelfand, I. M., Gelfand, S. I.: Algebraic vector bundles on P n and problems of linear algebra. (Russian) Funktsional. Anal. i Prilozhen., 12(3), 66–67 (1978)
Eisenbud, D., Fløystad, G., Schreyer, F.: Sheaf cohomology and free resolutions over exterior algebras. Trans. Amer. Math. Soc., 355(11), 4397–4426 (2003) (electronic)
Guo, J. Y, Wan, Q. H., Wu, Q. X.: Selfinjective Koszul algebras of finite complexity, preprint
Martínez-Villa, R., Zacharia, D.: Approximations with modules having linear resolutions. J. Algebra, 266(2), 671–697 (2003)
Ringel, Claus M. C.: Representation theory of algebras (Cocoyoc, 1994), CMS Conf. Proc., 18, Amer. Math. Soc., Providence, RI, 583–586, 1996
Beilinson, A., Ginzburg, V., Soergel, W.: Koszul duality patterns in representation theory. J. Amer. Math. Soc., 9(2), 473–527 (1996)
Green, Edward L., Martínez Villa, R.: Koszul and Yoneda algebras. Representation theory of algebras (Cocoyoc, 1994), CMS Conf. Proc., 18, Amer. Math. Soc., Providence, RI, 247–297, 1996
Guo, J. Y., Martínez-Villa, R., Takane, M.: Koszul generalized Auslander regular algebras. Algebras and Modules. II (Geiranger, 1996), CMS Conf. Proc., 24, Amer. Math. Soc., Providence, RI, 263–283, 1998
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professors Roberto Martínez–Villa and Raymondo Bautista on their 60th birthday
This research is supported in part by NSFC #10371036 and by Key Project #2A024 of the Provincial Ministry of Education of Hunan
Rights and permissions
About this article
Cite this article
Guo, J.Y., Li, B.J. & Wu, Q.X. On the Category of Koszul Modules of Complexity One of an Exterior Algebra. Acta Math Sinica 22, 849–854 (2006). https://doi.org/10.1007/s10114-005-0589-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-005-0589-2