Journal of Lie Theory

no. 2
The Variety of Lie Bialgebras
Journal of Lie Theory, Volume 13 (2003) no. 2, pp. 579-590
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.
DOI: 10.5802/jolt.322
Classification: 17B56, 17B62
Keywords: Lie bialgebra cohomology, cocycles 
@article{JOLT_2003_13_2_a16,
     author = {N. Ciccoli and L. Guerra},
     title = {The {Variety} of {Lie} {Bialgebras}},
     journal = {Journal of Lie Theory},
     pages = {579--590},
     year = {2003},
     volume = {13},
     number = {2},
     doi = {10.5802/jolt.322},
     zbl = {1038.17011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.322/}
}
TY  - JOUR
AU  - N. Ciccoli
AU  - L. Guerra
TI  - The Variety of Lie Bialgebras
JO  - Journal of Lie Theory
PY  - 2003
SP  - 579
EP  - 590
VL  - 13
IS  - 2
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.322/
DO  - 10.5802/jolt.322
ID  - JOLT_2003_13_2_a16
ER  - 
%0 Journal Article
%A N. Ciccoli
%A L. Guerra
%T The Variety of Lie Bialgebras
%J Journal of Lie Theory
%D 2003
%P 579-590
%V 13
%N 2
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.322/
%R 10.5802/jolt.322
%F JOLT_2003_13_2_a16
N. Ciccoli; L. Guerra. The Variety of Lie Bialgebras. Journal of Lie Theory, Volume 13 (2003) no. 2, pp. 579-590. doi: 10.5802/jolt.322

Cited by Sources: