Derived equivalences of DG algebras are not governed by their cohomology rings

2025/08/25 by Mao, X. -F., Lu, R. -K.
#16E45 #16E65 #16W20 #16W50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.17574

Abstract

Let \mathscrA and \mathscrB be two connected cochain DG algebra such that \mathscrA^#=\mathscrB^# and the cohomology rings H(\mathscrA) and H(\mathscrB) are isomorphic. We give examples to show that \mathscrA and \mathscrB are not necessarily derived equivalent, thereby answering to a question of Dugas.

Citations

• Homological properties of homologically smooth connected cochain DGAs
• Isomorphism problem and homological properties of DG free algebras
• Derived Picard groups of homologically smooth Koszul DG algebras
• Derived Picard groups of selfinjective Nakayama algebras
• Duality and Tilting for Commutative DG Rings
• Calabi-Yau algebras and superpotentials
• Calabi-Yau algebras and superpotentials
• Homological properties of cochain Differential Graded algebras
• Koszul differential graded algebras and BGG correspondence
• Formality of DG algebras (after Kaledin)
• Hochschild cohomology and derived Picard groups
• The Derived Picard Group is a Locally Algebraic Group
• Derived Picard Groups of Finite Dimensional Hereditary Algebras
• Dualizing Complexes, Morita Equivalence and the Derived Picard Group of a Ring

Related

• Duality for cochain DG algebras
• A note on homologically smooth connected cochain DG algebras
• Derived equivalences from cohomological approximations, and mutations of Φ-Yoneda algebras
• Homological properties of homologically smooth connected cochain DGAs
• Derived Picard groups of homologically smooth Koszul DG algebras