English

Braided Hom-Lie bialgebras

Quantum Algebra 2022-03-15 v9 Rings and Algebras

Abstract

We introduce the new concept of braided Hom-Lie bialgebras which is a generalization of Sommerh\"{a}user-Majid's braided Lie bialgebras and Yau's Hom-Lie bialgebras. Using this concept we give the unified product construction for Hom-Lie bialgebras which can be seen as a Hom-Lie version of Bespalov-Drabant's cocycle cross product bialgebras. Some special cases of unified products such as crossed product and matched pair of braided Hom-Lie bialgebras are investigated. As an application, we solve the Agore-Militaru extending problem for Hom-Lie bialgebras by using some non-abelian cohomology theory. Furthermore, one dimensional flag extending structures for Hom-Lie bialgebras are also investigated.

Keywords

Cite

@article{arxiv.0706.3282,
  title  = {Braided Hom-Lie bialgebras},
  author = {Tao Zhang},
  journal= {arXiv preprint arXiv:0706.3282},
  year   = {2022}
}
R2 v1 2026-06-21T08:41:03.686Z