Invariants along the recollements of Gorenstein derived categories

Abstract

In the paper, we show that a uniformly bounded and nonnegative triangle functor between Gorenstein derived categories of two CM-algebras induces a Gorenstein-projectively stable functor between the corresponding Gorenstein-projectively stable categories. Furthermore, we show that a ladder of Gorenstein derived categories of CM-finite algebras induces a recollement of Gorenstein-projectively stable categories under certain nice conditions. As a byproduct, a Gorenstein derived equivalence induces a Gorenstein-projectively stable equivalence for CM-finite Gorenstein algebras.

KEYWORDS:

• Gorenstein derived categories
• Gorenstein derived equivalences
• Gorenstein-projectively stable categories
• Gorenstein-projectively stable equivalences
• Gorenstein-projectively stable functors

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 18G25
• 16G10

Disclosure statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Funding

Supported by the National Natural Science Foundation of China (Grant No. 12271333).