Double Wreath Quasi-Hopf Algebras

Abstract: 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 quasi-Hopf algebras is obtained by deforming with a 2-cocycle the multiplication of a Radford biproduct quasi-Hopf algebra. Other classes of this type are given by the symplectic fermion quasi-Hopf algebras.

This is a joint work with D. Bulacu and D. Popescu.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

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