On Hom-Lie superbialgebras

Abstract

The purpose of this paper is to generalize to ${\mathbb{Z}}_2$-graded case the study of Hom-Lie bialgebras which were discussed first by D. Yau, then by C. Bai and Y. Sheng. We provide different ways for constructing Hom-Lie superbialgebras. Also we define Matched pairs, Manin supertriples and discuss their relationships. Moreover, we study coboundary and triangular Hom-Lie bialgebras, as well as infinitesimal deformations of the cobracket.

22 pages