k-step nilpotent Lie algebras
-
Michel Goze
and
Elisabeth Remm
Abstract
The 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 p-step nilpotent Lie algebras are obtained by contraction of the rigid ones.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- I2(u)-convergence of double sequences of order (α,β)
- Regular elements of the complete semigroups of binary relations of the class Σ6(X,8)
- On the limit properties of maximal likelihood estimators in a Hilbert space
- Shadowing and average shadowing properties for iterated function systems
- On almost increasing and quasi monotone sequences
- An unabelian version of the Voronov higher bracket construction
- Necessary and sufficient conditions for the ℍ-differentiability of quaternion functions
- k-step nilpotent Lie algebras
- An optimal control problem for a system of linear hyperbolic differential equations with constant coefficients
- On topologies in the family of sets with the Baire property
- On some inequalities for functions whose absolute values of the second derivatives are α-, m-, (α,m)-logarithmically convex
- On the cardinalities of at-sets in a real Hilbert space
- Higher-order Bernoulli and poly-Bernoulli mixed type polynomials
- On the existence of solutions for nonlocal boundary value problems
- fpn-injective and fpn-flat modules
- Algebroid functions with given Borel points
Articles in the same Issue
- Frontmatter
- I2(u)-convergence of double sequences of order (α,β)
- Regular elements of the complete semigroups of binary relations of the class Σ6(X,8)
- On the limit properties of maximal likelihood estimators in a Hilbert space
- Shadowing and average shadowing properties for iterated function systems
- On almost increasing and quasi monotone sequences
- An unabelian version of the Voronov higher bracket construction
- Necessary and sufficient conditions for the ℍ-differentiability of quaternion functions
- k-step nilpotent Lie algebras
- An optimal control problem for a system of linear hyperbolic differential equations with constant coefficients
- On topologies in the family of sets with the Baire property
- On some inequalities for functions whose absolute values of the second derivatives are α-, m-, (α,m)-logarithmically convex
- On the cardinalities of at-sets in a real Hilbert space
- Higher-order Bernoulli and poly-Bernoulli mixed type polynomials
- On the existence of solutions for nonlocal boundary value problems
- fpn-injective and fpn-flat modules
- Algebroid functions with given Borel points
