On The Formality Theorem for the Differential Graded Lie Algebra of Drinfeld

We discuss the differential graded Lie algebra (DGLA) of Drinfeld modeled on the tensor algebra of the universal enveloping algebra of a Lie algebra g over any field K of characteristic zero. We explicitly analyze the first obstruction to the existence of the formality quasi-isomorphism for this DGLA. Our analysis implies the formality of the DGLA of Drinfeld associated to the two-dimensional Borel algebra b.