kommutatoren
Kommutatoren (German for "commutators") are algebraic constructs that measure the failure of two elements to commute. The concept appears in several branches of mathematics and physics with closely related definitions and roles.
In group theory, the commutator of elements g and h is typically defined as [g,h] = g^{-1}h^{-1}gh. Commutators
In Lie algebras, the Lie bracket [X,Y] satisfies antisymmetry and the Jacobi identity; it generalizes commutators
In quantum mechanics operator commutators express fundamental relations and uncertainties. Canonical commutation relations such as [x,p]
Basic properties include antisymmetry (up to sign or inversion depending on context), bilinearity in linear settings,