Spin groupIn mathematics the spin group Spin(n) is a Lie group whose underlying manifold is the double cover of the special orthogonal group SO(n) = SO(n, R), such that there exists a short exact sequence of Lie groups (when n ≠ 2) The group multiplication law on the double cover is given by lifting the multiplication on . As a Lie group, Spin(n) therefore shares its dimension, n(n − 1)/2, and its Lie algebra with the special orthogonal group. For n > 2, Spin(n) is simply connected and so coincides with the universal cover of SO(n).
Satellite televisionSatellite television is a service that delivers television programming to viewers by relaying it from a communications satellite orbiting the Earth directly to the viewer's location. The signals are received via an outdoor parabolic antenna commonly referred to as a satellite dish and a low-noise block downconverter. A satellite receiver then decodes the desired television program for viewing on a television set. Receivers can be external set-top boxes, or a built-in television tuner.
Spin representationIn mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension and signature (i.e., including indefinite orthogonal groups). More precisely, they are two equivalent representations of the spin groups, which are double covers of the special orthogonal groups. They are usually studied over the real or complex numbers, but they can be defined over other fields. Elements of a spin representation are called spinors.
Free-to-airFree-to-air (FTA) services are television (TV) and radio services broadcast in unencrypted form, allowing any person with the appropriate receiving equipment to receive the signal and view or listen to the content without requiring a subscription, other ongoing cost, or one-off fee (e.g., pay-per-view). In the traditional sense, this is carried on terrestrial radio signals and received with an antenna.
Iron(III) chlorideIron(III) chloride describes the inorganic compounds with the formula (H2O)x. Also called ferric chloride, these compounds are available both in anhydrous and hydrated forms which are both hygroscopic. They are common sources of iron in its +3 oxidation state. The anhydrous derivative is a Lewis acid, while the hydrate is a mild oxidizing agent. It is used as a water cleaner and as an etchant for metals. All forms of ferric chloride are paramagnetic, owing to the presence of five unpaired electrons residing in 3d orbitals.
Iron(III)In chemistry, iron(III) refers to the element iron in its +3 oxidation state. In ionic compounds (salts), such an atom may occur as a separate cation (positive ion) denoted by Fe3+. The adjective ferric or the prefix ferri- is often used to specify such compounds, as in ferric chloride for iron(III) chloride (). The adjective ferrous is used instead for iron(II) salts, containing the cation Fe2+. The word ferric is derived from the Latin word ferrum, meaning "iron".
IronIron is a chemical element with the symbol Fe () and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, just ahead of oxygen (32.1% and 30.1%, respectively), forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust, being mainly deposited by meteorites in its metallic state, with its ores also being found there.
