Cohomology and 1-parameter formal 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.

20pages

References in corpus (7)

• Representations of hom-Lie algebras
• Hom-algebras and homology
• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• Hom-Lie 2-algebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Deformations of Hom-Alternative and Hom-Malcev algebras
• Multiplicative Hom-Lie superalgebra structures on infinite dimensional simple Lie superalgebras of vector fields

Cited by in corpus (5)

• Local cocycle 3-Hom-Lie Bialgebras and 3-Lie Classical Hom-Yang-Baxter Equation
• Weighted $\mathcal{O}$-operators on Hom-Lie triple systems
• Deformation Cohomology of Lie-Yamaguti algebras and Free Lie-Yamaguti algebras
• Cohomology of Leibniz Triple Systems and its applications
• Representations, extensions and deformations of $n$-BiHom-Lie algebras