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Higher Koszul complexes

Higher Koszul complexes
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摘要 In this paper we generalize the Koszul complexes and Koszul algebras, and introduce the higherKoszul (t-Koszul) complexes and higher Koszul algebras, where t ≥ 2 is an integer. We prove that an algebra ist-Koszul if and only if its t-Koszul complex is augmented, i.e. the higher degree (≥ 1) homologies vanish. Forarbitrary t-Koszul algebra , we also give a description of the structure of the cohomology algebra Ext ( 0, 0)by using the t-Koszul complexes, where the 0 is the direct sum of the simples. In this paper we generalize the Koszul complexes and Koszul algebras, and introduce the higher Koszul (t-Koszul) complexes and higher Koszul algebras, where t > 2 is an integer. We prove that an algebra is t-Koszul if and only if its t-Koszul complex is augmented, i.e. the higher degree (> 1) homologies vanish. For arbitrary t-Koszul algebra Λ we also give a description of the structure of the cohomology algebra Ext Λ ? (Λ 0, Λ 0) by using the t-Koszul complexes, where the Λ 0 is the direct sum of the simples
作者 叶郁 张璞
出处 《Science China Mathematics》 SCIE 2003年第1期118-128,共11页 中国科学:数学(英文版)
基金 This work was supported by the National Natural Science Foundation of China (Grant No. 19971080).
关键词 t-Koszul complex t-Koszul algebra. t-Koszul complex t-Koszul algebra
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参考文献4

  • 1Green,E. L.Martinez-Villa, R.Koszul and Yoneda algebras Ⅰ, Canad. Math. Soc[].Conf Proc.1996
  • 2Green,E. L.Martinez-Villa.R. Koszul and Yoneda algebras Ⅱ, Canad. Math. Soc[].Conf Proc.1998
  • 3Priddy,S.Koszul resolutions, Trans[].Journal of the American Mathematical Society.1970
  • 4Parshall,B. J.Koszul algebras and duality, Canad.Math. Soc[].Conf Proc.1995

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