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.

The variety of Lie bialgebras

CICCOLI, Nicola;GUERRA, Lucio
2003

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.
2003
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/118691
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