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

We introduce the Horn-analogue of the L-R-smash product and use it to define the Horn-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. (C) 2015 Elsevier Inc. All rights reserved.