有限维微分级数代数的反映完备性

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-10-03 DOI:10.1112/blms.13160

Isambard Goodbody

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引用次数: 0

摘要

我们将有限维代数的两个事实推广到有限维微分梯度代数。其一是中山引理，其二是单素体可以检测有限的射影维数。我们分别证明了与Gorenstein微分梯度代数和Koszul对偶有关的两个对偶版本。作为应用，我们证明了有限维微分梯度代数的一个可共表示性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Reflecting perfection for finite-dimensional differential graded algebras

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Reflecting perfection for finite-dimensional differential graded algebras

We generalise two facts about finite-dimensional algebras to finite-dimensional differential graded algebras. The first is the Nakayama lemma and the second is that the simples can detect finite projective dimension. We prove two dual versions which relate to Gorenstein differential graded algebras and Koszul duality, respectively. As an application, we prove a corepresentability result for finite-dimensional differential graded algebras.

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