【摘 要】
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In this paper we generalize the Koszul complexes and Koszul algebras, and introduce the higherKoszul (t-Koszul) complexes and higher Koszul algebras, where t ≥
【机 构】
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Department of Mathematics
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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.
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