Double wreath quasi-Hopf algebras

For a quasi-bialgebra H , we show that the category C of H- bimodules is duoidal and that the so called u-coaugmented bimonoids in C are exactly the quasi-bialgebras with a coalgebra projection. When H is a quasi-Hopf algebra with bijective antipode, we prove that the u-coaugmented bimonoids in C can also be described as what we will call double wreath quasi-Hopf algebras, objects determined by H and pre-bialgebras R within the category of Yetter-Drinfeld modules over H . A particular class of double wreath quasiHopf algebras is obtained by deforming with a 2-co cycle the multiplication of a Radford biproduct quasi-Hopf algebra. Other classes of this type are given by the symplectic fermion quasi-Hopf algebras. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.