Equivalences of higher derived brackets

This note elaborates on Th. Voronov’s construction [Th. Voronov, Higher derived brackets and homotopy algebras, J. Pure Appl. Algebra 202 (1–3) (2005) 133–153; Th. Voronov, Higher derived brackets for arbitrary derivations, Travaux Math. XVI (2005) 163–186] of L∞L∞-structures via higher derived brackets with a Maurer–Cartan element. It is shown that gauge equivalent Maurer–Cartan elements induce L∞L∞-isomorphic structures. Applications in symplectic, Poisson and Dirac geometry are discussed.