Lifting Lie algebras over the residue field of a discrete valuation ring Original Research Article

Let R be a discrete valuation ring with maximal ideal πR and residue field k. We study obstructions to lifting a Lie algebra image over R/πkR to one over R/πk+1R. If image is the Lie algebra over k obtained from reducing image then we show there exists a well-defined class in image which vanishes if and only if image lifts. Furthermore, if image lifts, the lifts are shown to be in one to one correspondence with image.