Recollements, Cohen-Macaulay Auslander algebras and Gorenstein projective conjecture

TL;DR

This paper demonstrates how certain recollements of derived categories of Cohen-Macaulay finite algebras induce recollements of their Auslander algebras and shows invariance of key conjectures under these recollements.

Contribution

It generalizes previous results by establishing a link between recollements of derived categories and Cohen-Macaulay Auslander algebras, and proves invariance of important conjectures.

Findings

A 4-recollement induces a 2-recollement of Cohen-Macaulay Auslander algebras.

Auslander-Reiten and Gorenstein projective conjectures are invariant under specific recollements.

The results extend the main theorem of Pan to a broader context.

Abstract

It is shown that a 4-recollement of derived categories of CM-finite algebras induces a 2-recollement of the corresponding Cohen-Macaulay Auslander algebras, which generalises the main theorem of Pan [S. Y. Pan, Derived equivalences for Cohen-Macaulay Auslander algebras, J. Pure Appl. Algebra 216 (2012), 355{363]. Moreover, both Auslander- Reiten conjecture and Gorenstein projective conjecture are shown invariant under 3 (or 4)-recollement of unbounded derived categories of algebras.