科研之友
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摘要
In this paper the problem of obstructions in Lie algebra deformations is studied from four different points of view. First, we illustrate the method of local ring, an alternative to Gerstenhaber's method for Lie deformations. We draw parallels between both methods showing that an obstruction class corresponds to a nilpotent local parameter of a versal deformation of the law in the scheme of Jacobi. Then, an elimination process in the global ring, which defines the scheme, allows us to obtain nilpotent elements and to describe the global method. Finally, the obstruction problem is studied in the geometry defined by generators and relations. Under certain conditions, we prove that subschemes of grassmannians of T-invariant ideals of a free Lie algebra (T being a torus of derivations), after quotient by an action group, are the same as those defined from Jacobi polynomials after a similar quotient.
- 出版日期2011
