Extension dimensions under singular equivalences and recollements

TL;DR

This paper investigates how extension dimensions of Artin algebras relate under recollements and singular equivalences, providing new inequalities and insights into their algebraic structure.

Contribution

It introduces new relationships and inequalities connecting extension dimensions through recollements and singular equivalences of Morita type with level.

Findings

Established inequalities among extension dimensions under recollements.

Linked extension dimensions via singular equivalences of Morita type with level.

Provided new bounds and relationships enhancing understanding of algebraic complexity.

Abstract

The extension dimensions of an Artin algebra give a reasonable way of measuring how far an algebra is from being representation-finite. In this paper we mainly study extension dimensions linked by recollements of derived module categories and singular equivalences of Morita type with level, and establish a series of new inequalities and relationships among their extension dimensions.