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We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras and we prove that they can be considered as the infinitesimal invariants of Lie groups endowed with a certain type of Jacobi structure. We also propose a method generalizing the Yang-Baxter equation method to obtain generalized Lie bialgebras. Finally, we classify the compact generalized Lie bialgebras.

Generalized Lie bialgebras and Jacobi structures on Lie groups