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Journal of Lie Theory 13 (2003), No. 2, 579--590
Copyright Heldermann Verlag 2003



The Variety of Lie Bialgebras

Nicola Ciccoli
Dip. di Matematica, UniversitÓ di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy

Lucio Guerra
Dip. di Matematica, UniversitÓ di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy



We define a Lie bialgebra cohomology as the total cohomology of a double complex constructed from a Lie algebra and its dual, we show that its 2-cocycles classify Lie bialgebra formal deformations and we prove the usual cohomological condition (i.e. H2 = 0) for formal rigidity. Lastly we describe the results of explicit computations in low-dimensional cases.

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