Topology of Lie groups | Spinors | Lie groups

Spin group

In mathematics the spin group Spin(n) 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) 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). The non-trivial element of the kernel is denoted −1, which should not be confused with the orthogonal transform of reflection through the origin, generally denoted −I. Spin(n) can be constructed as a subgroup of the invertible elements in the Clifford algebra Cl(n). A distinct article discusses the spin representations. (Wikipedia).

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“Spin” is one of the core building blocks of quantum reality, but it is a subtle concept to grasp. Here’s Brian Greene with one way to think about it. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Fac

From playlist Science Unplugged: Quantum Mechanics

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Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu

From playlist Science Unplugged: Quantum Mechanics

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From playlist Abstract algebra

Related pages

Clifford algebra | Seiberg–Witten theory | Covering groups of the alternating and symmetric groups | Graded (mathematics) | Lie group | Metaplectic group | Dynkin diagram | Point group | Supersymmetry | Simple Lie algebra | Special unitary group | Homotopy group | Spinor bundle | Hyperoctahedral group | Kernel (linear algebra) | Pin group | String group | Hypercube | Orientation entanglement | Isomorphism | Spin connection | Spin representation | Exact sequence | Quaternion | Definite quadratic form | Spinor | Dirac equation | Pauli exclusion principle | Root system | Electron | Eilenberg–MacLane space | Quotient group | Identity component | Endomorphism | Complexification | General linear group | Essential dimension | Table of Lie groups | SL2(R) | Spin structure | Indefinite orthogonal group | Tensor algebra | Connected space | Mathematics | Cross-polytope | Fermion | Covering group | Orthonormal basis | Riemannian manifold | Binary polyhedral group | Lie algebra | Closure operator | Binary octahedral group | Exterior algebra | Galois connection | Special linear group | Compact Lie algebra | Subgroup | Covering space | Orthogonal group | Binary tetrahedral group | Symplectic group | Exceptional isomorphism | Antiautomorphism | Clifford analysis | Maximal compact subgroup | Anyon | Affine connection | Center (group theory)