Twisted Forms of Differential Lie Algebras over $${\\mathbb {C}}(t)$$C(t) Associated with Complex Simple Lie Algebras

Abstract

Discussed here is descent theory in the differential context where everything is equipped with a differential operator. To answer a question personally posed by A.\xa0Pianzola, we determine all twisted forms of the differential Lie algebras over \n$${\\mathbb {C}}(t)$$\n\n associated with complex simple Lie algebras. Hopf–Galois Theory, a ring-theoretic counterpart of theory of torsors for group schemes, plays a role when we grasp the above-mentioned twisted forms from torsors.