Recollements of Cohen-Macaulay Auslander algebras and Gorenstein derived categories

Abstract

Let $A$, $B$ and $C$ be associative rings with identity. Using a result of Koenig we show that if we have a $\mathbb{D}^{\rm{b}}({\rm{mod\mbox{-}}} )$ level recollement, writing $A$ in terms of $B$ and $C$, then we get a $\mathbb{D}^-({\rm{Mod\mbox{-}}} )$ level recollement of certain functor categories, induces from the module categories of $A$, $B$ and $C$. As an application, we generalise the main theorem of Pan [Sh. Pan, Derived equivalences for Cohen-Macaulay Auslander algebras, J. Pure Appl. Algebra, 216 (2012), 355-363] in terms of recollements of Gorenstein artin algebras. Moreover, we show that being Gorenstein as well as being of finite Cohen-Macaulay type, are invariants with respect to $\mathbb{D}^{\rm{b}}_{{{\mathcal{G}p}}}({\rm{mod\mbox{-}}})$ level recollements of virtually Gorenstein algebras, where ${\mathbb{D}}_{\mathcal{G}p}^{\mathrm{b}}$ denotes the Gorenstein derived category.

This paper has been withdrawn by the author due to some mistakes

References in corpus (2)

• Derived equivalences for $\Phi$-Auslander-Yoneda algebras
• Jordan Hölder theorems for derived module categories of piecewise hereditary algebras