2020/02/24 by Fernández, David, Herscovich, Estanislao
#14A22 #16E45 #17B63 #18G55 #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2002.10495
In this article we prove that double quasi-Poisson algebras, which are non-commutative analogues of quasi-Poisson manifolds, naturally give rise to pre-Calabi-Yau algebras. This extends one of the main results in [11] (see also [10]), where a relationship between pre-Calabi-Yau algebras and double Poisson algebras was found. However, a major difference between the pre-Calabi-Yau algebra constructed in the mentioned articles and the one constructed in this work is that the higher multiplications indexed by even integers of the underlying A∞-algebra structure of the pre-Calabi-Yau algebra associated to a double quasi-Poisson algebra do not vanish, but are given by nice cyclic expressions multiplied by explicitly determined coefficients involving the Bernoulli numbers.