Geodesic
The Variety of Lie Bialgebras
Nicola Ciccoli1 ; Lucio Guerra1, 2, 3, 4
1Dip. di Matematica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
2We 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. H
3= 0) for formal rigidity. Lastly we describe the results of explicit computations in low-dimensional cases.
4[
Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 579-590 
Nicola Ciccoli; Lucio Guerra. The Variety of Lie Bialgebras. Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 579-590. http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a16/
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     author = {Nicola Ciccoli and Lucio Guerra},
     title = {The {Variety} of {Lie} {Bialgebras}},
     journal = {Journal of Lie Theory},
     pages = {579--590},
     year = {2003},
     volume = {13},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a16/}
}
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Voir la notice de l'article provenant de la source Heldermann Verlag

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.