Abstract
The purpose of this paper is to generalize to -graded case the study of Hom-Lie bialgebras which were discussed first by D. Yau, then by Y. Sheng and C. Bai. We first provide various constructions of Hom-Lie superbialgebras and a classification of 3-dimensional Hom-Lie superbialgebras with 2-dimensional even part. Moreover, we study coboundary and triangular Hom-Lie superbialgebras, as well as infinitesimal deformations of the cobracket. Furthermore, following Sheng and Bai we define matched pairs, Manin supertriples and discuss their relationships.
Acknowledgments
The authors are thankful and grateful to the anonymous referee for remarks and recommendations.