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

## TL;DR

This paper extends Poisson-Lie symmetry and T-duality to Jacobi-Lie structures, presenting new dual sigma models on Lie groups with potential implications for quantum theories.

## Contribution

It introduces Jacobi-Lie symmetry and T-duality, generalizing existing concepts to broader mathematical structures and providing new models and examples.

## Key findings

- New Jacobi-Lie T-dual sigma models constructed
- Examples demonstrating the generalized duality
- Potential insights into quantum aspects of T-duality

## 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.