Physics

Pure mathematics

Nilpotent group

Dimension (graph theory)

Mathematics

Statistics

Algebra over a field

Variety (cybernetics)

Artificial intelligence

Indecomposable module

Rigidity (electromagnetism)

Class (philosophy)

Computer science

Lie algebra

Quantum mechanics

Nilpotent

Lie conformal algebra

Algebra Colloquium

In this note we consider 2-step nilpotent Lie algebras and give a criterion for the rigidity of this class in the variety [Formula: see text] of 2-step nilpotent Lie algebras of dimension n. We apply this criterion to prove that every rigid Lie algebra in [Formula: see text] is indecomposable, except for [Formula: see text] 3 ⊕ ℂ and [Formula: see text] 3 ⊕ [Formula: see text] 3 .

On Rigid 2-Step Nilpotent Lie Algebras