Journal of Lie Theory, 7(2), 287-292 (1997)

Lie bialgebras and cohomology

M. Benayed

Université des Sciences de Lille
UFR de Mathématiques Pures
URA 751 associée au CNRS
F-59655 Villeneuve d'Ascq Cedex
Abstract: Let $\scriptstyle\g$ be a finite dimensional real Lie bialgebra. We introduce a $\scriptstyle\R$-valued cohomology of $\scriptstyle\g$ such that the space of all inequivalent Lie bialgebra central extensions of $\scriptstyle\g$ by $\scriptstyle\R$ is isomorphic to the second group of this cohomology. Furthermore, we study the natural projection of this group on the $\scriptstyle\R$-valued Lie algebra second cohomology group of $\scriptstyle\g$.

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