Ciccoli, Nicola; Guerra, Lucio The variety of Lie bialgebras. (English) Zbl 1038.17011 J. Lie Theory 13, No. 2, 579-590 (2003). Authors’ abstract: 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. \(H^2= 0\)) for formal rigidity. Lastly we describe the results of explicit computations in low-dimensional cases. Reviewer: Said Benayadi (Metz) MSC: 17B56 Cohomology of Lie (super)algebras 17B62 Lie bialgebras; Lie coalgebras Keywords:Lie bialgebra cohomology; cocycles PDFBibTeX XMLCite \textit{N. Ciccoli} and \textit{L. Guerra}, J. Lie Theory 13, No. 2, 579--590 (2003; Zbl 1038.17011) Full Text: EuDML