9 papers
Braided Hopf algebroids and Lie algebroids
Xiao Han
We construct braided Hopf algebroids in a braided monoidal category over a field and study its properties using graphical representation. Then we study Ehresmann-Schauenburg Ho…
Cleft Extensions for Hopf Algebroids without Antipodes
Xiao Han, Peter Schauenburg
We introduce cleft extensions for Hopf algebroids. We prove the equivalence between cleft extensions, -twisted crossed products, and Hopf-Galois extensions with the normal basis…
Coquasi-bialgebroids and cocycle twisting
Xiao Han, Shahn Majid
We introduce coquasi-bialgebroids over a noncommutative base algebra. Using Takeuchi's \(\times_B\)-coalgebra formalism, we require the coproduct to remain an algebra map into the…
Hopf BiGalois Theory for Hopf Algebroids
Xiao Han, Peter Schauenburg
We develop a theory of Hopf BiGalois extensions for Hopf algebroids. We understand these to be left bialgebroids (whose left module categories are monoidal categories) fulfilling a…
Quantum jet Hopf algebroids by cotwist
Xiao Han, Shahn Majid
We introduce a cotwist construction for Hopf algebroids that also entails cotwisting or `quantisation' of the base and which is dual to a previous twisting construction of P. Xu. W…
*-Hopf algebroids
Edwin Beggs, Xiao Han, Shahn Majid
We introduce a theory of -structures for bialgebroids and Hopf algebroids over a -algebra, defined in such a way that the relevant category of (co)modules is a bar category.…
Hopf Galois extensions of Hopf algebroids
Xiao Han, Peter Schauenburg
We study Hopf Galois extensions of Hopf algebroids as a generalization of the theory for Hopf algebras. More precisely, we introduce (skew-)regular comodules and generalize the str…
On bicrossed modules of Hopf algebras
Xiao Han
We use Hopf algebroids to formulate a notion of a noncommutative and non-cocommutative Hopf 2-algebra. We show how these arise from a bicrossproduct Hopf algebra with Peiffer ident…
Hopf bimodules and Yetter-Drinfeld modules of Hopf algebroids
Xiao Han
We construct Hopf bimodules and Yetter-Drinfeld modules of Hopf algebroids as a generalization of the theory for Hopf algebras. More precisely, we show that the categories of Hopf…