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 Rinvariant 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 



10834362
 
Volume/pages 



14:2(2009), p. 287317
 
ISI 



000265943000002
 
Full text (Publisher's DOI) 


  
Full text (publisher's version  intranet only) 


  
