论文标题
$ \ operatorName {ext} $ - 双重扩展代数的标准模块代数
The $\operatorname{Ext}$-algebra of standard modules over dual extension algebras
论文作者
论文摘要
我们在$ \ operatorname {ext} $ - algebra $ \ operatorName {ext}_λ^\ ast（δ，Δ）$之间的$ \ operatoRatorname {ext} $ - algebra $ \ aperatorname {ext} $ - extementiondembra $λ$λ $ \ operatotorName {ext} $ - algebra $ \ operatatorName {ext} _b^\ ast（\ mathbb {l}，\ mathbb {l}）$ at $ a $。这些$ \ operatoRatorname {ext} $ - 代数有天然的$ a_ \ infty $ - 结构，在$ b $上的某些技术假设下，我们在$ \ permatatorName {ext}_λ^ast（ext}_λ^ast（δ）$上完全描述了这一点。 $ \ operatatorName {ext} _b^\ ast（\ mathbb {l}，\ mathbb {l}）$。例如，我们在$ b = a = a = k \ mathbb {a} _n /（\ propatorAtorName {rad} k \ mathbb {a} a} _n）_n）^\ ell $的情况下明确计算这些$ a_ \ infty $ - 结构。
We exhibit an isomorphism of associative algebras between the $\operatorname{Ext}$-algebra $\operatorname{Ext}_Λ^\ast(Δ,Δ)$ of standard modules over the dual extension algebra $Λ$ of two directed algebras $B$ and $A$ and the dual extension algebra of the $\operatorname{Ext}$-algebra $\operatorname{Ext}_B^\ast(\mathbb{L},\mathbb{L})$ with $A$. There are natural $A_\infty$-structures on these $\operatorname{Ext}$-algebras, and, under certain technical assumptions on $B$, we describe that on $\operatorname{Ext}_Λ^\ast(Δ,Δ)$ completely in terms of that on $\operatorname{Ext}_B^\ast(\mathbb{L},\mathbb{L})$. As an example, we compute these $A_\infty$-structures explicitly in the case where $B=A=K\mathbb{A}_n /(\operatorname{rad}K\mathbb{A}_n)^\ell$.
