Poisson-Lie T-Duality and Bianchi Type Algebras

TL;DR

This paper classifies Bianchi bialgebras, constructs their Drinfeld doubles, and develops sigma-models with Poisson-Lie symmetry, providing explicit examples of dual models.

Contribution

It introduces a systematic construction of sigma-models with Poisson-Lie symmetry based on Bianchi bialgebras and their Drinfeld doubles, including explicit dual model examples.

Findings

All Bianchi bialgebras have been classified.

Drinfeld doubles constructed using invariant inner products.

Explicit Poisson-Lie dual models demonstrated.

Abstract

All Bianchi bialgebras have been obtained. By introducing a non-degenerate adjoint invariant inner product over these bialgebras the associated Drinfeld doubles have been constructed, then by calculating the coupling matrices for these bialgebras several sigma-models with Poisson-Lie symmetry have been obtained. Two simple examples as prototypes of Poisson-Lie dual models have been given.