WEAKLY DISCRETE KOSZUL MODULES, II

Year 2012, Volume: 12 Issue: 12, 1 - 11, 01.12.2012

Yuan Pan

Abstract

This paper is a continuous work of “Y. Pan, Weakly discrete
Koszul modules, submitted, (2011)” ([12]), where the so-called weakly discrete
Koszul module was first introduced. In this paper, the Ext module of
a weakly discrete Koszul module is studied. Further, as the application of
the approximation chain theorem obtained in [12], we will study the relations
of the minimal graded projective resolutions between a given weakly discrete
Koszul module and its quotients.

Keywords

discrete Koszul algebras, discrete Koszul modules, weakly discrete Koszul modules

References

• A. Beilinson, V. Ginszburg and W. Soergel, Koszul duality patterns in repre- sentation theory, J. Amer. Math. Soc., 9 (1996), 473-525.
• N. Bian, Y. Ye and P. Zhang, Generalized d-Koszul modules, Math. Res. Lett., (2) (2011), 191-200.
• E.L. Green and E.N. Marcos, δ-Koszul algebras, Comm. Algebra, 33 (2005), 1764.
• E. L. Green, E. N. Marcos, R. Mart´ınez-Villa and Pu Zhang, D-Koszul alge- bras, J. Pure Appl. Algebra, 193 (2004), 141-162.
• E. L. Green and R. Mart´ınez-Villa, Koszul and Yoneda algebras, Representa- tion theory of algebras (Cocoyoc, 1994), CMS Conference Proceedings, Amer- ican Mathematical Society, Providence, RI, 18 (1996), 247-297.
• R. Mart´ınez-Villa and D. Zacharia, Approximations with modules having linear resolutions, J. Algebra, 266 (2003), 671-697.
• J.-F. L¨u, On modules with piecewise-Koszul towers, Houston J. Math., 35(1), (2009), 185-207.
• J.-F. L¨u, Weakly piecewise-Koszul modules, (China) Adv. Math., (2011), in press.
• J.-F. L¨u and M.-S. Chen, Discrete Koszul algebras, Algebr. Represent. Theory, (2010), in press.
• J.-F. L¨u, J.-W. He and D.-M Lu, Piecewise-Koszul algebras, Sci. China Ser. A, (12) (2007), 1785-1794.
• J.-F. L¨u, J.-W. He and D.-M Lu, On modules with d-Koszul towers, Chinese Ann. Math., 28A(2) (2007), 231-238.
• Y. Pan, Weakly discrete Koszul modules, submitted, (2011).
• S. Priddy, Koszul resolutions, Trans. Amer. Math. Soc., 152 (1970), 39-60.
• C. A. Weibel, An Introduction to Homological Algebra, Cambridge Studies in Avanced Mathematics, 38, Cambridge Univ. Press, 1995. Yuan Pan
• Yiwu Industrial and Commercial College Yiwu, Zhejiang 322000 P.R. China e-mail: [e-mail]