Braided Hopf algebras and gauge transformations

We study infinitesimal gauge transformations of K -equivariant noncommutative prin- cipal bundles, for K a triangular Hopf algebra. They form a Lie algebra of derivations in the category of K -modules. We study Drinfeld twist deformations of these infinitesi- mal gauge transformations. We give several examples from abelian and Jordanian twist deformations. These include the quantum Lie algebra of gauge transformations of the 4 instanton bundle and of the orthogonal bundle on the quantum \theta 4-sphere.