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The aim of this paper is to extend to Hom-algebra structures the theory offormal deformations of algebras which was introduced by Gerstenhaber forassociative algebras and extended to Lie algebras by Nijenhuis-Richardson. Wedeal with Hom-associative and Hom-Lie algebras. We construct the first groupsof a deformation cohomology and give several examples of deformations. Weprovide families of Hom-Lie algebras deforming Lie algebra $sl_2$ and describeas formal deformations the q-deformed Witt algebra and Jackson $sl_2$.

Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras