# Some dimensions of DG polynomial algebras

## TL;DR

This paper investigates various homological dimensions of a specific class of differential graded polynomial algebras, providing explicit calculations for their DG Krull, global, ghost, and Rouquier dimensions.

## Contribution

It explicitly determines multiple homological dimensions of cochain DG polynomial algebras with polynomial underlying graded algebra.

## Key findings

- DG Krull dimension computed
- Global dimension determined
- Ghost and Rouquier dimensions calculated

## Abstract

Assume that $\mathcal{A}$ is a cochain DG polynomial algebra such that its underlying graded algebra $\mathcal{A}^{#}$ is a polynomial algebra generated by $n$ degree $1$ elements. We determine the DG Krull dimension, the global dimension, the ghost dimension and the Rouquier dimension of $\mathcal{A}$.