DEGENERATIONS OF 7-DIMENSIONAL NILPOTENT LIE ALGEBRAS

By Dietrich Burde. 2004

52 citations recorded by the source corpus.

ABSTRACT We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is the use of trivial and adjoint cohomology of these algebras. In addition, we give some new results on the varieties of complex Lie algebra laws in low dimension.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8cc596609871a74672a5df0aa7227f6fc9924970

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Manuel Ceballos
2. Y. Volkov
3. Ivan Kaygorodov
4. Dietrich Burde
5. Wolfgang Alexander Moens
6. Alice Fialowski

In Geometry and Topology

1. Manuel Ceballos
2. Y. Volkov
3. Ivan Kaygorodov
4. Dietrich Burde
5. Wolfgang Alexander Moens
6. Alice Fialowski

In Mathematical Physics

1. Manuel Ceballos
2. Y. Volkov
3. Ivan Kaygorodov
4. Dietrich Burde
5. Wolfgang Alexander Moens
6. Alice Fialowski

Citations in the corpus

• The Variety of Two-dimensional Algebras Over an Algebraically Closed Field (2017, background): “Degenerations are an interesting subject, which was studied in various papers (see, for example, [3–7, 10–12, 14–16, 18, 20, 21, 25–27, 29]).”
• Abelian Ideals of Maximal Dimension for Solvable Lie Algebras (2009, methodology): “α ∈ C [e 1,e 2] = e 2, [e 1,e 3] = e 2 +αe 3, [e 1,e 4] = (α +1)e 4, [e 2,e 3] = e 4 Proof. The proof is straightforward, using a classification of low-dimensional Lie algebras, e.g., the one given in [5]. Note that g 4(α) ≃ g 4(β) if and only if αβ = 1 or α = β. 5. NilpotentLie algebras In a nilpote”