A sufficient condition for a connected DG algebra to be Calabi-Yau

Abstract

Assume that A is a connected cochain DG algebra such that the trivial DG algebra $(H(A),0)$ is a Calabi-Yau DG algebra. We show that A is also a Calabi-Yau DG algebra. As applications, we study the Calabi-Yau property of a connected cochain DG algebra A when H(A) belongs to certain types of 3-Calabi-Yau graded algebras.

Keywords:

• Calabi-Yau
• cohomology graded algebra
• connected Cochain DG algebra
• Gorenstein
• homologically smooth
• Koszul

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 16E10
• 16E30
• 16E45
• 16E65

Additional information

Funding

X.-F. Mao is supported by the National Natural Science Foundation of China (No. 11871326 and No. 11771272), by the China Postdoctoral Science Foundation (No. 20090450066), by the China Postdoctoral Science Foundation (No. 201003244), and by Key Disciplines of Shanghai Municipality (S30104). The authors thank the referee for his/her careful reading of this paper.