Higher Koszul complexes

【摘要】 <正> 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 A, we also give a description of the structure of the cohomology algebra Ext∧ (∧o, ∧o) by using the t-Koszul complexes, where the Ao is the direct sum of the simples.更多还原

【Abstract】 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 A, we also give a description of the structure of the cohomology algebra Ext∧ (∧o, ∧o) by using the t-Koszul complexes, where the Ao is the direct sum of the simples.更多还原