Journal of Lie Theory

no. 3
Unified Products for Braided Lie Bialgebras with Applications
Journal of Lie Theory, Volume 32 (2022) no. 3, pp. 671-696
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.
DOI: 10.5802/jolt.1246
Classification: 17B62, 18D35
Keywords: Lie bialgebra, braided Lie bialgebras, unified product, non-abelian cohomology, Yetter-Drinfeld modules 
@article{JOLT_2022_32_3_a2,
     author = {T. Zhang},
     title = {Unified {Products} for {Braided} {Lie} {Bialgebras} with {Applications}},
     journal = {Journal of Lie Theory},
     pages = {671--696},
     year = {2022},
     volume = {32},
     number = {3},
     doi = {10.5802/jolt.1246},
     zbl = {1522.17031},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1246/}
}
TY  - JOUR
AU  - T. Zhang
TI  - Unified Products for Braided Lie Bialgebras with Applications
JO  - Journal of Lie Theory
PY  - 2022
SP  - 671
EP  - 696
VL  - 32
IS  - 3
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1246/
DO  - 10.5802/jolt.1246
ID  - JOLT_2022_32_3_a2
ER  - 
%0 Journal Article
%A T. Zhang
%T Unified Products for Braided Lie Bialgebras with Applications
%J Journal of Lie Theory
%D 2022
%P 671-696
%V 32
%N 3
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1246/
%R 10.5802/jolt.1246
%F JOLT_2022_32_3_a2
T. Zhang. Unified Products for Braided Lie Bialgebras with Applications. Journal of Lie Theory, Volume 32 (2022) no. 3, pp. 671-696. doi: 10.5802/jolt.1246

Cited by Sources: