Solvable Lie Algebras with Nilradicals of Orthogonal Types

Recently certain twisted Lie algebras, so-called Hom-Lie algebras, and their duals have been considered in the literature.In this paper we investigate boundary and quasi-triangular Hom-Lie bialgebras further.In particular, we characterize the quasi-triangularity of boundary Hom-Lie bialgebras in terms of both a certain Hom-Lie algebra morphism and a certain Hom-Lie coalgebra morphism.We also give a necessary and sufficient condition for a given Hom-Lie algebra and a given 2-tensor to admit a coboundary Hom-Lie bialgebra structure.Finally, we generalize the Drinfeld double of a Lie bialgebra to Hom-Lie bialgebras and discuss the dual codouble.