Free summands of conormal modules and central elements in 
homotopy lie algebras of local rings
S. Iyengar

Abstract.
If Q-->R is a surjective homomorphism of noetherian local 
ring such that the kernel is contained in the square of 
the maximal ideal of Q, and the conormal module for the 
homomorphism has a free summand of rank n, then the degree 
2 central subspace of the homotopy Lie algebra of R has 
dimension greater than or equal to n. This is a corollary 
of the Main Theorem of this note. The techniques involved 
provide new proofs of some well known results concerning 
the conormal module.