Jacobi–Lie symmetry and Jacobi–Lie T-dual sigma models on group manifolds

Abstract

Using the concept of Jacobi–Lie group and Jacobi–Lie bialgebra, we generalize the definition of Poisson–Lie symmetry to Jacobi–Lie symmetry. In this regard, we generalize the concept of Poisson–Lie T-duality to Jacobi–Lie T-duality and present Jacobi–Lie T-dual sigma models on Lie groups, which have Jacobi–Lie symmetry. Using this symmetry, new cases of duality appear and some examples are given. This generalization may provide insights to understand the quantum features of Poisson–Lie T-duality, in a more satisfactory way.