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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.CT2025
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…