Extensions abéliennes des bigèbres de Lie

Abstract: In this paper we generalize the results about central extensions of Lie bialgebras obtained in [3] to the case of abelian extensions, i.e. to extensions with abelian, but not necessarily central, kernel. An explicit classification of such extensions is given, and the question of the realizability of the classifying space as a (second) cohomology group is adressed. The realizability question is answered in the affirmative in the case of one dimensional kernel, generalizing a result for central extensions given in [4]. For higher dimensional kernel the classifying space does not in general admit a group structure, it may even be empty. However, if this classifying space is not empty, then it can be described by what one may call a non abelian cohomology of Lie bialgebras.

Full text of the article:

• Compressed DVI file (22291 Bytes)
• Compressed Postscript file (47258 Bytes)