Cartan subalgebra

A Cartan subalgebra is a special type of algebraic structure used in mathematics, particularly in the fields of Lie algebras and theoretical physics. It refers to a maximal set of commuting elements within a Lie algebra, meaning they can be thought of as independent "directions" that don't interfere with each other. This concept helps mathematicians and physicists understand symmetries and various physical systems, such as particle behavior in quantum mechanics. Essentially, it provides a framework to analyze complex structures by breaking them down into simpler, non-conflicting components.