CENTRAL ELEMENTS AND DEFORMATIONS OF LOCAL-RINGS

The following question raised by Avranov is proved to have a positive answer in the case when (S, n) is an equi-characteristic local ring with n(3) = 0. Suppose there is a central element of degree at least two in the homotopy Lie algebra of the local ring S, is it true that there is another local ring (R, m) with a non-zero divisor f epsilon m(2) such that S congruent to R/(f)? We also give a positive answer to this if S is a ''Foberg'' ring (also called a Koszul algebra) and the central element has degree two. We use minimal models in the proofs and for the second result the paper is self-contained.