Publication
Title
Versal deformations and versality in central extensions of Jacobi schemes
Author
Abstract
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.
Language
English
Source (journal)
Transformation groups
Publication
2009
ISSN
1083-4362
Volume/pages
14:2(2009), p. 287-317
ISI
000265943000002
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 24.02.2012
Last edited 05.11.2017
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