Homological properties of homologically smooth connected cochain DGAs

2024/07/20 by Mao, X. -F. · 1 citation
#16E10 #16E45 #16E65 #16W50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2407.14805

Abstract

Assume that \mathscrA is a connected cochain DG algebra. We show that \mathscrA is homologically smooth and Gorenstein if and only if its Ext-algebra H(R\Hom_\mathscrA(\mathbbmk,\mathbbmk)) is a Frobenius graded algebra. Moreover, \mathscrA is Calabi-Yau if and only if the Ext-algebra H(R\Hom_\mathscrA(\mathbbmk,\mathbbmk)) is a symmetric Frobenius graded algebra. These generalize the corresponding results in \citeHW1 and \citeHM, where the additional Koszul hypothesis is needed.

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