Differential graded Lie algebras and singularities of level sets of momentum mappings

The germ of an analytic variety X at a point xelement ofX is said to be quadratic if it is bi-analytically isomorphic to the germ of a cone defined by a system of homogeneous quadratic equations at the origin. Arms, Marsden and Moncrief (1981) show that under certain conditions the analytic germ of a level set of a momentum mapping is quadratic. We discuss related ideas in a more algebraic context by associating to an affine Hamiltonian action an differential graded Lie algebra, which in the presence of an invariant positive complex structure, is formal in the sense of Deligne, Griffiths, Morgan and Sullivan (1975). (orig.)