One-parameter formal deformations of Hom-Lie-Yamaguti algebras

TL;DR

This paper investigates one-parameter formal deformations of Hom-Lie-Yamaguti algebras, extending cohomology theories and analyzing their roles in deformation and rigidity properties.

Contribution

It introduces cohomology groups for Hom-Lie-Yamaguti algebras and examines their relevance to deformation theory, including infinitesimals and rigidity.

Findings

First and second cohomology groups relate to deformation theory and rigidity.

Third cohomology group does not serve as an obstruction in deformations.

Extended cohomology groups generalize those of Lie-Yamaguti algebras.

Abstract

This paper studies one-parameter formal deformations of Hom-Lie-Yamaguti algebras. The first, second and third cohomology groups on Hom-Lie-Yamaguti algebras extending ones on Lie-Yamaguti algebras are provided. It is proved that first and second cohomology groups are suitable to the deformation theory involving infinitesimals, equivalent deformations and rigidity. However, the third cohomology group is not suitable for the obstructions.