Dominant dimensions of two classes of finite dimensional algebras

TL;DR

This paper investigates the dominant dimension of hereditary and tree algebras, providing explicit formulas to understand their homological properties and differences.

Contribution

It introduces explicit formulas for the dominant dimension of hereditary and tree algebras, advancing the theoretical understanding of their structure.

Findings

Derived explicit formulas for dominant dimensions

Enhanced understanding of algebraic homological properties

Compared dominant dimensions across algebra classes

Abstract

The aim of this paper is to study the dominant dimension of two important classes of finite dimensional algebras, namely, hereditary algebras and tree algebras. We derive an explicit formula for the dominant dimension of each class.