Classical r-matrices of real low-dimensional Jacobi-Lie bialgebras and their Jacobi-Lie groups

Abstract

In this research we obtain the classical r-matrices of real two and three dimensional Jacobi-Lie bialgebras. In this way, we classify all non-isomorphic real two and three dimensional coboundary Jacobi-Lie bialgebras and their types (triangular and quasitriangular). Also, we obtain the generalized Sklyanin bracket formula by use of which, we calculate the Jacobi structures on the related Jacobi-Lie groups. Finally, we present a new method for constructing classical integrable systems using coboundary Jacobi-Lie bialgebras.

arXiv comment23 pages

References in corpus (7)

• Generalized Lie bialgebroids and Jacobi structures
• Poisson-Lie T-Duality and Bianchi Type Algebras
• Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups
• Classification of two and three dimensional Lie super-bialgebras
• The gl(1|1) Lie superbialgebras
• Classical r-matrices of two and three dimensional Lie super-bialgebras and their Poisson-Lie supergroups
• Jacobi Structures in ${\mathbb{R}}^3$

Cited by in corpus (5)

• Invariant Poisson-Nijenhuis structures on Lie groups and classification
• Jacobi-Lie symmetry and Jacobi-Lie T-dual sigma models on group manifolds
• Jacobi-Lie T-plurality
• Classification of real low dimensional Jacobi(generalized)-Lie bialgebras
• Jacobi-Lie Hamiltonian systems on real low-dimensional Jacobi-Lie groups and their Lie symmetries