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Title
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Versal deformations and versality in central extensions of Jacobi schemes
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Transformation groups
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Publication
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2009
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ISSN
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1083-4362
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DOI
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10.1007/S00031-009-9057-X
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Volume/pages
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14
:2
(2009)
, p. 287-317
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ISI
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000265943000002
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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