This research introduces a new cohomology for lie bialgebras, showing connections to central extensions and implications for algebraic structures.
Let g be a finite dimensional real Lie bialgebra.We introduce an R -valued cohomology of g for which the space of all inequivalent Lie bialgebra central extensions of g by R is isomorphic to that second cohomology group of g .Furthermore, we study the natural projection of this group on the R -valued Lie algebra second cohomology group of g .
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M. Benayed (1997) studied this question.
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