Journal of Lie Theory 13 (2003), No. 2, 579--590
Copyright Heldermann Verlag 2003
The Variety of Lie Bialgebras
Nicola Ciccoli
Dip. di Matematica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
Lucio Guerra
Dip. di Matematica, Università 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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