Classification of real low dimensional Jacobi(generalized)-Lie bialgebras

Abstract

We describe the definition of Jacobi (generalized)-Lie bialgebras $((\mathbf{g},{\varphi }_0),({\mathbf{g}}^{\ast },X_0))$ in terms of structure constants of the Lie algebras $\mathbf{g}$ and ${\mathbf{g}}^{\ast }$ and components of their 1-cocycles $X_0\in \mathbf{g}$ and ${\varphi }_0\in {\mathbf{g}}^{\ast }$ in the basis of the Lie algebras. Then, using adjoint representations and automorphism Lie groups of Lie algebras, we give a method for classification of real low dimensional Jacobi-Lie bialgebras. In this way, we obtain and classify real two and three dimensional Jacobi-Lie bialgebras.

14 pages

References in corpus (1)

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

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• Jacobi-Lie Models and Supergravity Equations
• Plane-parallel waves as Jacobi-Lie models
• On spectator dependence of Jacobi-Lie T-plurality