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
基金
This work was supported by the National Natural Science Foundation of China (Grant No. 19971080).
