2025/09/26 by Gustavo Jasso, Jasso, Gustavo, Fernando Muro +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2509.22625
Let d be a positive integer. In a previous article we established a bijective correspondence between the following classes of objects, considered up to the appropriate notion of equivalence: differential graded algebras (dg) with finite-dimensional 0-th cohomology such that the canonical generator of their perfect derived category is a basic d\ZZ-cluster tilting object, and basic Frobenius algebras that are twisted (d+2)-periodic as bimodules. In this article, we prove a variant of our general correspondence for bimodule right Calabi--Yau dg algebras. A novel ingredient is a new cohomology theory which contains obstructions to the existence and uniqueness of minimal A_∞-bimodule structures on a graded bimodule. As an application of our results, we obtain, to our knowledge, the first example of an algebraic triangulated category with a triangulated Calabi--Yau structure that cannot be lifted to a bimodule right Calabi--Yau structure on any of its dg enhancements.