Equivalences of Higher Derived Brackets

Abstract

This note elaborates on Th. Voronov's construction [math/0304038,math/0412202] of $L_{\infty }$-structures via higher derived brackets with a Maurer-Cartan element. It is shown that gauge equivalent Maurer-Cartan elements induce $L_{\infty }$-isomorphic structures. Applications in symplectic, Poisson and Dirac geometry are discussed.

16 pages; minor changes; corrected typos; to appear in JPAA

References in corpus (3)

• Deformations of coisotropic submanifolds and strong homotopy Lie algebroids
• Generalized Kahler and hyper-Kahler quotients
• Graded Poisson Algebras

Cited by in corpus (14)

• Poincaré--Birkhoff--Witt isomorphisms and Kapranov dg-manifolds
• Introduction to graded geometry
• Homotopy Batalin-Vilkovisky algebras
• Nonabelian higher derived brackets
• Formality and Kontsevich--Duflo type theorems for Lie pairs
• BFV-complex and higher homotopy structures
• Superfield Hamiltonian quantization in terms of quantum antibrackets
• Representation of a gauge field via intrinsic "BRST" operator
• Nijenhuis forms on $L_{\infty }$-algebras and Poisson geometry
• On coisotropic deformations of holomorphic submanifolds
• Equivalences of coisotropic submanifolds
• Quantum antibrackets: polarization and parametrization
• The Deformation $L_{\infty }$ algebra of a Dirac--Jacobi structure
• Deformations of Courant Algebroids and Dirac Structures via Blended Structures