Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld   double of a Hom-Hopf algebra
  We introduce the Hom-analogue of the L-R-smash product and use it to define the Hom-analogue of the diagonal crossed product. When H is a finite dimensional Hom-Hopf algebra with bijective antipode and bijective structure map, we define the Drinfeld double of H; its algebra structure is a Hom-diagonal crossed product and it has all expected properties, namely it is quasitriangular and modules over it coincide with left-right Yetter-Drinfeld modules over H. 
Abdenacer Makhlouf, Florin Panaite
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