Pre-Calabi-Yau algebras were introduced in the last decade by M. Kontsevich, A. Takeda and Y. Vlassopoulos using the necklace bracket. This notion is equivalent to a cyclic A∞-algebra for the natural bilinear form in the finite-dimensional case. Moreover, W-K. Yeung showed that double Poisson DG structures provide an example of pre-Calabi-Yau structures. In 2020, D. Fernandez and E. Herscovich proved that given a morphism of double Poisson DG algebras from A to B, one can produce a cyclic A∞-algebra and A∞-morphisms between the latter and the cyclic A∞-algebras associated to A and B. I will explain how to generalize this result to pre-Calabi-Yau algebras by doing an explicit construction of a (cyclic) A∞-algebra and A∞-morphisms given a pre-Calabi-Yau morphism.
This talk relates to this arXiv paper.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
