Double Quasi-Poisson Algebras are Pre-Calabi-Yau

Abstract In this article, we prove that double quasi-Poisson algebras, which are noncommutative analogues of manifolds, naturally give rise to pre-Calabi-Yau algebras. This extends one the main results in [11], where a correspondence between certain algebras and Poisson was found (see also [13, 12, 10]). However, major difference algebra constructed mentioned articles work is higher multiplications indexed by even integers underlying $A_{\infty }$-algebra structure associated with do not vanish, but given nice cyclic expressions multiplied explicitly determined coefficients involving Bernoulli numbers.