Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Lightning strikeA lightning strike is a lightning event in which the electric discharge takes place between the atmosphere and the ground. Most originate in a cumulonimbus cloud and terminate on the ground, called cloud-to-ground (CG) lightning. A less common type of strike, ground-to-cloud (GC) lightning, is upward-propagating lightning initiated from a tall grounded object and reaching into the clouds. About 25% of all lightning events worldwide are strikes between the atmosphere and earth-bound objects.
LightningLightning is a natural phenomenon formed by electrostatic discharges through the atmosphere between two electrically charged regions, either both in the atmosphere or with one in the atmosphere and on the ground, temporarily neutralizing these in a near-instantaneous release of an average of one gigajoule of energy. This discharge may produce a wide range of electromagnetic radiation, from heat created by the rapid movement of electrons, to brilliant flashes of visible light in the form of black-body radiation.
Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Irreducible representationIn mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of . Every finite-dimensional unitary representation on a Hilbert space is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.
Electromagnetic pulseAn electromagnetic pulse (EMP), also referred to as a transient electromagnetic disturbance (TED), is a brief burst of electromagnetic energy. The origin of an EMP can be natural or artificial, and can occur as an electromagnetic field, as an electric field, as a magnetic field, or as a conducted electric current. The electromagnetic interference caused by an EMP can disrupt communications and damage electronic equipment. An EMP such as a lightning strike can physically damage objects such as buildings and aircraft.
Electromagnetic compatibilityElectromagnetic compatibility (EMC) is the ability of electrical equipment and systems to function acceptably in their electromagnetic environment, by limiting the unintentional generation, propagation and reception of electromagnetic energy which may cause unwanted effects such as electromagnetic interference (EMI) or even physical damage to operational equipment. The goal of EMC is the correct operation of different equipment in a common electromagnetic environment. It is also the name given to the associated branch of electrical engineering.
Algebra representationIn abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint functors page); there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra.
Lie algebra representationIn the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space together with a collection of operators on satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators.
Compact groupIn mathematics, a compact (topological) group is a topological group whose topology realizes it as a compact topological space (when an element of the group is operated on, the result is also within the group). Compact groups are a natural generalization of finite groups with the discrete topology and have properties that carry over in significant fashion. Compact groups have a well-understood theory, in relation to group actions and representation theory. In the following we will assume all groups are Hausdorff spaces.
