Braided Hom-Lie bialgebras
Abstract
We introduce the new concept of braided Hom-Lie bialgebras which is a generalization of Sommerh\"auser-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.
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