2020/12/29 by Bandiera, Ruggero
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2012.14812
We explore the relationship between the classical constructions of cumulants and Koszul brackets, showing that the former are an expontial version of the latter. Moreover, under some additional technical assumptions, we prove that both constructions are compatible with standard homological perturbation theory in an appropriate sense. As an application of these results, we provide new proofs for the homotopy transfer Theorem for L_∞ and IBL_∞ algebras based on the symmetrized tensor trick and the standard perturbation Lemma, as in the usual approach for A_∞ algebras. Moreover, we prove a homotopy transfer Theorem for commutative BV_∞ algebras in the sense of Kravchenko which appears to be new. Along the way, we introduce a new definition of morphism between commutative BV_∞ algebras.