Derived equivalences between matrix subrings and their applications

TL;DR

This paper establishes derived equivalences between matrix subrings and applies these results to compute dimensions and verify conjectures for specific algebra classes.

Contribution

It introduces new derived equivalences for matrix subrings and uses them to analyze global and finitistic dimensions, confirming the finitistic dimension conjecture for certain algebra classes.

Findings

Calculated global and finitistic dimensions of matrix subrings

Verified the finitistic dimension conjecture for Harada and tiled triangular algebras

Established derived equivalences between specific matrix subrings

Abstract

In this paper, we construct derived equivalences between matrix subrings. As applications, we calculate the global dimensions and the finitistic dimensions of some matrix subrings. And we show that the finitistic dimension conjecture holds for a class of Harada algebras and a class of tiled triangular algebras.