  Lie admissible algebra structures, called center-symmetric algebras, are
defined. Main properties and algebraic consequences are derived and discussed.
Bimodules are given and used to build a center-symmetric algebra on the direct
sum of underlying vector space and a finite dimensional vector space. Then, the
matched pair of center-symmetric algebras is established and related to the
matched pair of sub-adjacent Lie algebras. Besides, Manin triple of
center-symmetric algebras is defined and linked with their associated matched
pairs. Further, center-symmetric bialgebras of center-symmetric algebras are
investigated and discussed. Finally, a theorem yielding the equivalence between
Manin triple of center-symmetric algebras, matched pairs of Lie algebras and
center-symmetric bialgebras is provided.
