Semisimple Lie algebra

A semisimple Lie algebra is a mathematical structure that describes symmetrical properties and transformations, especially in geometry and physics. It can be thought of as a collection of operations that combine smoothly, with no small, "degenerate" parts—meaning it's built from simple, non-reducible components that are tightly interconnected. These algebras have no abelian (commutative) ideals, which simplifies their analysis and classification. They underpin much of modern physics, like understanding fundamental particles and forces, and are essential in the study of symmetry in mathematics and science.