Quasi-Lie bialgebroids and twisted Poisson manifolds

TL;DR

This paper develops a homological framework for quasi-Lie bialgebroids, generalizing quasi-Lie bialgebras and twisted Poisson structures relevant in string theory, providing a new perspective on their mathematical structure.

Contribution

It introduces a homological approach to quasi-Lie bialgebroids, extending the theory of quasi-Lie bialgebras and twisted Poisson structures with applications in string theory.

Findings

Established a homological formulation of quasi-Lie bialgebroids

Connected quasi-Lie bialgebroids to twisted Poisson structures

Provided a new mathematical framework for structures in string theory

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 \v{S}evera and Weinstein using a different method.