scholarly journals Transformation groups on real plane and their differential invariants

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Maryna O. Nesterenko
Keyword(s):  
Lie Algebras ◽  
Differential Invariants ◽  
Transformation Groups ◽  
Real Plane ◽  
Continuous Transformation ◽  
The Real ◽  
Finite Dimensional ◽  
Complete Sets ◽  
Finite Dimensional Lie Algebras ◽  
Invariant Differentiation

Complete sets of bases of differential invariants, operators of invariant differentiation, and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of finite-dimensional Lie algebras on the real plane are revisited.

scholarly journals k-step nilpotent Lie algebras

2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Michel Goze ◽  
Elisabeth Remm
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Deformation Process ◽  
Nilpotent Lie Algebras ◽  
Early Stages ◽  
Finite Dimensional ◽  
Contraction Process ◽  
Finite Dimensional Lie Algebras

AbstractThe classification of complex or real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example, the nilpotent Lie algebras are classified only up to dimension 7. Moreover, to recognize a given Lie algebra in the classification list is not so easy. In this work, we propose a different approach to this problem. We determine families for some fixed invariants and the classification follows by a deformation process or a contraction process. We focus on the case of 2- and 3-step nilpotent Lie algebras. We describe in both cases a deformation cohomology for this type of algebras and the algebras which are rigid with respect to this cohomology. Other

Inequalities for the second cohomology of finite dimensional Lie algebras

2013 ◽  
Vol 142 (1) ◽  
pp. 121-127
Author(s):  
Ali Reza Salemkar ◽  
Behrouz Edalatzadeh ◽  
Hamid Mohammadzadeh
Keyword(s):  
Lie Algebras ◽  
Finite Dimensional ◽  
Finite Dimensional Lie Algebras

scholarly journals Quasi-state rigidity for finite-dimensional Lie algebras

2017 ◽  
Vol 221 (1) ◽  
pp. 25-57
Author(s):  
Michael Björklund ◽  
Tobias Hartnick
Keyword(s):  
Lie Algebras ◽  
Finite Dimensional ◽  
Finite Dimensional Lie Algebras
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