Journal of Lie Theory 32 (2022), No. 3, 671--696
Copyright Heldermann Verlag 2022
Unified Products for Braided Lie Bialgebras with Applications
Tao Zhang
College of Mathematics and Information Science, Henan Normal University, Xinxiang, P. R. China
zhangtao@htu.edu.cn
We construct unified products for braided Lie bialgebras. Some special cases of unified products such as crossed product and matched pair of braided Lie bialgebras are studied. It is proved that the extending problem for Lie bialgebras can be classified by some non-abelian cohomology theory of braided Lie bialgebras. As a byproduct, a non-abelian extension theory of Lie bialgebras is developed. Furthermore, one dimensional flag extending systems of Lie bialgebras are also investigated.
Keywords: Lie bialgebra, braided Lie bialgebras, unified product, non-abelian cohomology, Yetter-Drinfeld modules.
MSC: 17B62, 18D35.
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