Versal deformations and versality in central extensions of Jacobi schemesVersal deformations and versality in central extensions of Jacobi schemes
Faculty of Sciences. Mathematics and Computer Science

Department of Mathematics - Computer Sciences

article

2009 2009

Mathematics

Transformation groups

14(2009):2, p. 287-317

1083-4362

000265943000002

E

English (eng)

University of Antwerp

Let L(m) be the scheme of the laws defined by the Jacobi identities on K(m) with K a field. A deformation of g is an element of L(m), parametrized by a local ring A, is a local morphism from the local ring of L(m) at phi(m) to A. The problem of classifying all the deformation equivalence classes of a Lie algebra with given base is solved by "versal" 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) = R (sic) phi(n) in L(m) and its nilpotent radical phi(n) in the R-invariant scheme L(n)(R) with reductive part R, under some conditions. So the versal deformations of phi(m) in L(m) are deduced from those of phi(n) in L(n)(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.

https://repository.uantwerpen.be/docman/iruaauth/302a97/09f1320.pdf

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