Three homological invariants under cleft extensions

TL;DR

This paper studies how certain homological invariants like Igusa-Todorov distances, extension, and Rouquier dimensions change under cleft extensions of abelian categories, with applications to various algebraic structures.

Contribution

It provides new insights into the behavior of homological invariants under cleft extensions and applies these results to specific algebraic constructions.

Findings

Igusa-Todorov distances are preserved under certain cleft extensions

Extension and Rouquier dimensions exhibit specific behaviors in these contexts

Applications include Morita context rings and trivial extension rings

Abstract

In this paper, we investigate the behavior of Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories. We apply our results to Morita context rings, trivial extension rings, tensor rings and arrow removals.