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 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.

Keywords:

• Coboundary Hom-Lie superbialgebra
• Hom-Lie superalgebra
• Manin supertriple
• matched pair
• triangular Hom-Lie superbialgebra

2010 Mathematics subject classification:

• 17B62
• 17B37

Acknowledgments

The authors are thankful and grateful to the anonymous referee for remarks and recommendations.