Differential calculus on Hopf-Galois extension via the Durdevic braiding

Abstract: We introduce a class of first-order differential calculus on principal comodule algebras generated by the Durdevic braiding $σ$ and a chosen vertical ideal. Starting from the universal calculus and a strong connection, we construct $σ$-generated calculus and prove their existence for arbitrary principal comodule algebras. We show that, in this setting, connection $1$-forms and vertical maps descend to the quotient calculus and are compatible with the induced braided symmetry. We also compare this framework with Durdevic's complete differential calculus.