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- W2952858440 abstract "Let $L_m$ be the scheme of the laws defined by the Jacobi's identities on $K^m$ with $K$ a field. A deformation of $ginL_m$, parametrized by a local $K$-algebra $A$, is a local $K$-algebra morphism from the local ring of $L_m$ at $phi_m$ to $A$. The problem to classify all the deformation equivalence classes of a Lie algebra with given base is solved by deformations. First, we give an algorithm for computing versal deformations. Second, we prove there is a bijection between the deformation equivalence classes of an algebraic Lie algebra $phi_m=mathrm{R}ltimesphi_n$ in $L_m$ and its nilpotent radical $phi_n$ in the $mathrm{R}$-invariant scheme $L_n^{mathrm{R}}$ with reductive part $mathrm{R}$, under some conditions. So the versal deformations of $phi_m$ in $L_m$ is deduced to those of $phi_n$ in $L_n^{mathrm{R}}$, which is a more simple problem. Third, we study versality in central extensions of Lie algebras. Finally, we calculate versal deformations of some Lie algebras." @default.
- W2952858440 created "2019-06-27" @default.
- W2952858440 creator A5053510489 @default.
- W2952858440 creator A5074373281 @default.
- W2952858440 date "2010-09-03" @default.
- W2952858440 modified "2023-09-27" @default.
- W2952858440 title "Versal Deformations and Versality in Central Extensions of Jacobi's Schemes" @default.
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