We determine and study all Lie bialgebra central extensions of R²ⁿ by R admitting the Heisenberg algebra H_2n+1 as the underlying Lie algebra structure. The present work answers the question about the realizability of Lie bialgebra structures on H_2n+1 as central extensions of R²ⁿ endowed with the adapted Lie bialgebra structure, by R.

The first author would like to thank G. Tuynman for discussions. The second author would like to thank G. Tuynman for the hospitality at Université de Lille I, and also C. Brezinski and J. Mikram, principal investigators of the grant Action Intégrée A/I 1036.