We introduce a notion generalizing Calabi–Yau structures on A-infinity algebras and
categories, which we call pre-Calabi–Yau structures. This notion does not need either one of …

We establish a system of formal noncommutative calculus for differential forms and
polyvector fields, which forms the foundations for the study of pre-Calabi-Yau categories …

In this article we prove that there exists a relation between d-pre-Calabi-morphisms
introduced by M. Kontsevich, A. Takeda and Y. Vlassopoulos and cyclic A∞-morphisms …

We introduce the notion of double Courant–Dorfman algebra and prove that it satisfies the
so-called Kontsevich–Rosenberg principle, that is, a double Courant–Dorfman algebra …

We introduce the notions of shifted bisymplectic and shifted double Poisson structures on
differential graded associative algebras, and more generally on non-commutative derived …

A double Poisson bracket, in the sense of M. Van den Bergh, is an operation on an
associative algebra A which induces a Poisson bracket on each representation space Rep …

In this article, we prove that double quasi-Poisson algebras, which are noncommutative
analogues of quasi-Poisson manifolds, naturally give rise to pre-Calabi-Yau algebras. This …

In this article we prove that there exists a relation between $ d $-pre-Calabi-Yau morphisms
introduced by M. Kontsevich, A. Takeda and Y. Vlassopoulos and cyclic $ A_ {\infty} …

The main goal of this thesis is to provide a systematic study of several integrable systems
defined on complex Poisson manifolds associated to extended cyclic quivers. These spaces …

There is a functor P: pCYd→ ̂ A∞ sending a d-pre-Calabi-Yau structure on A to the cyclic
A∞-structure on A⊕ A∗[d− 1] given in Theorem 2 and a d-pre-Calabi-Yau morphism sd+ 1 …