Central extensions and deformations of Hom-Lie triple systems

ABSTRACT

In this paper, we study the cohomology theory of Hom-Lie triple systems generalizing the Yamaguti cohomology theory of Lie triple systems. We introduce the central extension theory for Hom-Lie triple systems and show that there is a one-to-one correspondence between equivalent classes of central extensions of Hom-Lie triple systems and the third cohomology group. We develop the 1-parameter formal deformation theory of Hom-Lie triple systems and prove that it is governed by the cohomology group.

KEYWORDS:

• Central extension
• cohomology
• deformation
• Hom-Lie triple system

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 17A40
• 17B10
• 17B56
• 55U15

Acknowledgments

The authors would like to thank the referee for valuable comments and suggestions on this article.