nilpotent Lie algebra

A nilpotent Lie algebra is a mathematical structure where, as you repeatedly combine elements using a specific operation called a Lie bracket, the results eventually become zero after a finite number of steps. Think of it as a system that simplifies itself to nothing when you apply these operations enough times. This property indicates a high level of internal symmetry and "degeneracy," making nilpotent Lie algebras important in understanding certain geometric and algebraic problems, especially where gradual simplifications or hierarchical structures are involved.