Derived equivalences for hereditary Artin algebras

详细信息    查看全文

• 作者：Donald Stanley^a ; ^{donald.stanley@uregina.ca" class="auth_mail" title="E-mail the corresponding author} ; Adam-Christiaan van Roosmalen^b ; ^{adamchristiaan.vanroosmalen@uhasselt.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：16E35 ; 16E60 ; 16G10 ; 18E30
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：5 November 2016
• 年：2016
• 卷：303
• 期：Complete
• 页码：415-463
• 全文大小：807 K

文摘

We study the role of the Serre functor in the theory of derived equivalences. Let A$\mathcal{A}$ be an abelian category and let (U,V)$(\mathcal{U},\mathcal{V})$ be a t  -structure on the bounded derived category D^bA$D^b\mathcal{A}$ with heart H$\mathcal{H}$. We investigate when the natural embedding H→D^bA$\mathcal{H}\to D^b\mathcal{A}$ can be extended to a triangle equivalence D^bH→D^bA$D^b\mathcal{H}\to D^b\mathcal{A}$. Our focus of study is the case where A$\mathcal{A}$ is the category of finite-dimensional modules over a finite-dimensional hereditary algebra. In this case, we prove that such an extension exists if and only if the t  -structure is bounded and the aisle U$\mathcal{U}$ of the t-structure is closed under the Serre functor.