DG polynomial algebras and their homological properties

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（4）
• 页码范围: 629-648
• 页数: 20页
• 语种: 英文

摘要

In this paper,we introduce and study differential graded (DG for short) polynomial algebras.In brief,a DG polynomial algebra A is a connected cochain DG algebra such that its underlying graded algebra A#is a polynomial algebra K[x1,x2,...,xn] with ｜xi｜ =1 for any i ∈ {1,2,...,n}.We describe all possible differential structures on DG polynomial algebras,compute their DG automorphism groups,study their isomorphism problems,and show that they are all homologically smooth and Gorenstein DG algebras.Furthermore,it is proved that the DG polynomial algebra A is a Calabi-Yau DG algebra when its differential (e)A ≠ 0 and the trivial DG polynomial algebra (A,0) is Calabi-Yau if and only if n is an odd integer.