Nonabelian higher derived brackets

Equivalences of Higher Derived Brackets

This note elaborates on Th. Voronov’s construction [V1, V2] of L∞-structures via higher derived brackets with a Maurer–Cartan element. It is shown that gauge equivalent Maurer–Cartan elements induce L∞-isomorphic structures. Applications in symplectic, Poisson and Dirac geometry are discussed.

Higher Derived Brackets and Deformation Theory

The existing constructions of derived Lie and sh-Lie brackets involve multilinear maps that are used to define higher order differential operators. In this paper, we prove the equivalence of three different definitions of higher order operators. We then introduce a unifying theme for building derived brackets and show that two prevalent derived Lie bracket constructions are equivalent. Two basi...

Algebraic aspects of higher nonabelian Hodge theory

Higher Poisson Brackets and Differential Forms

We show how the relation between Poisson brackets and symplectic forms can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential forms). In particular we arrive at a notion which is a generalization of a symplectic structure and gives rise to higher Poisson brackets. We also obtain a construction of Koszul type brackets in this s...

Derived brackets and sh Leibniz algebras

We will give a generalized framework of derived bracket construction. It will be shown that a deformation differential provides a strong homotopy (sh) Leibniz algebra structure by derived bracket construction. A relationship between the three concepts, homotopy algebra theory, deformation theory and derived bracket construction, will be discussed. We will prove that the derived bracket construc...