commutator identity

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• Commutator — This article is about the mathematical concept. For the relation between canonical conjugate entities, see canonical commutation relation. For the type of electrical switch, see commutator (electric). In mathematics, the commutator gives an… …   Wikipedia

• Commutator subgroup — In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.[1][2] The commutator subgroup is important because it is the smallest… …   Wikipedia

• commutator — noun a) an electrical switch, in a generator or motor, that periodically reverses the direction of an electric current b) (of a group) an element of the form ghgh where g and h are …   Wiktionary

• Jacobi identity — In mathematics the Jacobi identity is a property that a binary operation can satisfy which determines how the order of evaluation behaves for the given operation. Unlike for associative operations, order of evaluation is significant for… …   Wikipedia

• Lie algebra — In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term… …   Wikipedia

• Matrix mechanics — Quantum mechanics Uncertainty principle …   Wikipedia

• Trace (linear algebra) — In linear algebra, the trace of an n by n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii represents the entry on the ith row and ith column …   Wikipedia

• Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …   Wikipedia

• Lie group — Lie groups …   Wikipedia

• Triple system — In algebra, a triple system is a vector space V over a field F together with a F trilinear map: (cdot,cdot,cdot) colon V imes V imes V o V.The most important examples are Lie triple systems and Jordan triple systems. They were introduced by… …   Wikipedia

• Uncertainty principle — In quantum physics, the Heisenberg uncertainty principle states that locating a particle in a small region of space makes the momentum of the particle uncertain; and conversely, that measuring the momentum of a particle precisely makes the… …   Wikipedia