论文标题
$ 3 $二维DG Sklyanin代数的同源性能
Homological properties of $3$-dimensional DG Sklyanin algebras
论文作者
论文摘要
在本文中，我们介绍了DG Sklyanin代数的概念，这些代数是连接的Cochain DG代数，其基本分级代数为Sklyanin代数。令$ \ Mathcal {a} $为$ 3 $ - 二维DG Sklyanin代数，带有$ \ Mathcal {a}^{\＃} = s_ {a，b，c} $，$（a，a，b，b，b，b，c）\ in \ bbb in \ bbb {p} $ \ mathfrak {d} = \ {（1,0,0），（0,1,0），（0,0,1）\} \ sqcup \ {（a，a，b，c）| a^3 = b^3 = b^3 = c^3 = c^3 \}。尤其是，我们找出分别为calabi-yau，koszul，gorenstein和同源性平滑的$ \ mathcal {a} $的条件。
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 $\mathcal{A}$ be a $3$-dimensional DG Sklyanin algebra with $\mathcal{A}^{\#}=S_{a,b,c}$, where $(a,b,c)\in \Bbb{P}_k^2-\mathfrak{D}$ and $$\mathfrak{D}=\{(1,0,0), (0,1,0),(0,0,1)\}\sqcup\{(a,b,c)|a^3=b^3=c^3\}.$$ We systematically study its differential structures and various homological properties. Especially, we figure out the conditions for $\mathcal{A}$ to be Calabi-Yau, Koszul, Gorenstein and homologically smooth, respectively.
