×

The variety of Lie bialgebras. (English) Zbl 1038.17011

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.

MSC:

17B56 Cohomology of Lie (super)algebras
17B62 Lie bialgebras; Lie coalgebras
PDFBibTeX XMLCite
Full Text: EuDML