Homological properties of 3-dimensional DG Sklyanin algebras

Abstract

In this paper, we introduce the notion of DG Sklyanin algebras, which are connected cochain DG algebras whose underlying graded algebras are Sklyanin algebras. Let [Formula: see text] be a [Formula: see text]-dimensional DG Sklyanin algebra with [Formula: see text], where [Formula: see text] and [Formula: see text] We systematically study its differential structures and various homological properties. Especially, we figure out the conditions for [Formula: see text] to be Calabi–Yau, Koszul, Gorenstein and homologically smooth, respectively.