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math.QA2026
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…
math.CT2026
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…
math.QA2026
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…