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

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.