Some dimensions of DG polynomial algebras

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 one elements. We determine the DG Krull dimension, the global dimension, the ghost dimension, and the Rouquier dimension of $\mathcal{A}.$

Keywords:

• Phrases
• DG polynomial algebra
• Krull dimension
• global dimension
• ghost dimension
• Rouquier dimension

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 16E10
• 16E45
• 16E65
• 16W20
• 16W50

Additional information

Funding

The first author is supported by the National Natural Science Foundation of China (NSFC, Grant No. 11871326) and the Innovation Program of Shanghai Municipal Education Commission (Grant No. 12YZ031).