Quasi-Lie bialgebroids and twisted Poisson manifolds

Abstract

We develop a theory of quasi-Lie bialgebroids using a homological approach. This notion is a generalization of quasi-Lie bialgebras, as well as twisted Poisson structures with a 3-form background which have recently appeared in the context of string theory, and were studied by Ševera and Weinstein using a different method.

The souped-up published version: section on gauge transformations and a few other remarks added. added

References in corpus (2)

• Courant algebroids, derived brackets and even symplectic supermanifolds
• Nonassociative Star Product Deformations for D-brane Worldvolumes in Curved Backgrounds

Cited by in corpus (16)

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• Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids
• Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
• Quasi-Hamiltonian groupoids and multiplicative Manin pairs
• Leibniz bialgebras, relative Rota-Baxter operators and the classical Leibniz Yang-Baxter equation
• Finite deformations from a heterotic superpotential: holomorphic Chern--Simons and an $L_{\infty }$ algebra
• Quasiclassical Lian-Zuckerman Homotopy Algebras, Courant Algebroids and Gauge Theory
• Star products on graded manifolds and ${\alpha }^{\prime }$-corrections to Courant algebroids from string theory
• Modular classes of regular twisted Poisson structures on Lie algebroids
• Nijenhuis and Compatible Tensors on Lie and Courant algebroids
• Hyperstructures on Lie algebroids
• On Jacobi quasi-Nijenhuis algebroids and Courant-Jacobi algebroid morphisms
• On quasi-Jacobi and Jacobi-quasi bialgebroids
• Courant bracket twisted both by a 2-form $B$ and by a bi-vector $\theta$
• Split Courant algebroids as $L_{\infty }$-structures
• Derived brackets and sh Leibniz algebras