Differential graded Lie algebras and singularities of level sets of momentum mappings
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The germ of an analytic varietyX at a pointx∈X is said to bequadratic 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 show in  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 a differential graded Lie algebra, which in the presence of an invariant positive complex structure, is formal in the sence of .
KeywordsNeural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing
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