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We introduce the Hom-analogue of the L-R-smash product and use it to definethe Hom-analogue of the diagonal crossed product. When H is a finitedimensional Hom-Hopf algebra with bijective antipode and bijective structuremap, we define the Drinfeld double of H; its algebra structure is aHom-diagonal crossed product and it has all expected properties, namely it isquasitriangular and modules over it coincide with left-right Yetter-Drinfeldmodules over H.

Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld double of a Hom-Hopf algebra