The homological determinant conjecture for noetherian connected graded AS Gorenstein algebras

Let AA be a noetherian connected graded Artin-Schelter Gorenstein algebra, and let μA\mu_A denote its Nakayama automorphism. Let hdet\operatorname{hdet} denote the homological determinant. The homological determinant conjecture. One has

hdet(μA)=1.\operatorname{hdet}(\mu_A)=1.

This conjecture was made in the cited earlier work, and the theorem immediately preceding it proves the assertion when AA satisfies the epsilon-condition; the supplied text does not establish the conjecture for every algebra in its stated class.

Sources & referencesView supporting material

Primary source

Manuel Reyes, Daniel Rogalski and James J. Zhang, “Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras”, arXiv:1408.0536 (2016).

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