Formal Deformations, Contractions and Moduli Spaces of Lie Algebras (original) (raw)
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In this talk I consider deformations of algebraic structures. The notion of 1-parameter deformation is due to Gerstenhaber. Here I give a generalization of the classical notion by considering deformations with a commutative algebra base, and define the miniversal formal deformation. This notion is necessary to describe non-equivalent deformations with the same infinitesimal part, and to find singular nontrivial deformations with zero infinitesimal part. I use the example of a vector field Lie algebra to demonstrate the computation. Another example which underlines the importance of such general deformations is to consider moduli spaces of Lie algebras. This I also demonstrate on an example.
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