Central elements and deformations of local rings (Q1313783)

Let \((R,m)\) be a local equicharacteristic ring with \(m^ 3=0\). If there exists a central element of degree at least two in the homotopy Lie algebra, then \((R,m)\) is an embedded deformation of a ring \(S\), which means that there is a non-zero-divisor \(f\in m^ 2\) such that \(S\simeq R/(f)\). This answers a question raised by L. L. Avramov. The proof uses the notion of minimal models for a ring.