Bialgebra structures on the Heisenberg algebra

We classify, up to isomorphism, those exact bialgebra structures on the (2n + 1) - dimensional Heisenberg algebra which satisfy the classical Yang-Baxter equation. In the case n = 1, we classify all bialgebra structures and describe the singular locus and the symplectic leaves of the corresponding Lie-Poisson structure on the Heisenberg group.

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