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Infinitesimal deformation theory of Lie-Yamaguti algebras was introduced byTao Zhang and Juan Li . We extend their theory to develop formal one-parameterdeformation theory of Lie-Yamaguti algebras. It turns out that the rightdeformation cohomology which controls deformations in this context, is avariant of Lie-Yamaguti algebra cohomology. At the end, we introduce the freeLie-Yamaguti algebra and prove that it is rigid.

Formal one parameter deformation of Lie-Yamaguti algebras