In mathematics the spinor group or spin group Spin(n) is a particular double cover of the special orthogonal group SO(n, R). That is, there exists a short exact sequence of Lie groups Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... In mathematics, specifically topology, a covering map is a continuous surjective map p : C → X, with C and X being topological spaces, which has the following property: to every x in X there exists an open neighborhood U such that p -1(U) is a union of mutually disjoint open... In mathematics, the orthogonal group of degree n over a field F (written as O(n,F)) is the group of n-by-n orthogonal matrices with entries from F, with the group operation that of matrix multiplication. ... In mathematics, especially in homological algebra and other applications of Abelian category theory, as well as in group theory, an exact sequence is a (finite or infinite) sequence of objects and morphisms between them such that the image of one morphism equals the kernel of the next. ... In mathematics, a Lie group (IPA ) is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ...

For n > 2, Spin(n) is simply connected and so coincides with the universal cover of SO(n, R). As a Lie group Spin(n) therefore shares its dimension, n(n−1)/2, and its Lie algebra with the special orthogonal group. A geometrical object is called simply connected if it consists of one piece and doesnt have any circle-shaped holes or handles. Higher-dimensional holes are allowed. ... In mathematics, specifically topology, a covering map is a continuous surjective map p : C → X, with C and X being topological spaces, which has the following property: to every x in X there exists an open neighborhood U such that p -1(U) is a union of mutually disjoint open... In mathematics, a Lie algebra is an algebraic structure whose main use lies in studying geometric objects such as Lie groups and differentiable manifolds. ...

Spin(n) can be constructed as a subgroup of the invertible elements in the Clifford algebra C(n). In group theory, given a group G under a binary operation *, we say that some subset H of G is a subgroup of G if H also forms a group under the operation *. More precisely, H is a subgroup of G if the restriction of * to H is a group... Clifford algebras are a type of associative algebra in mathematics. ...

See also: spinor, spinor bundle, anyon, pin group, spin structure. In mathematics and physics, in particular in the theory of the orthogonal groups, spinors are certain kinds of mathematical objects (group representations of Spin(N), roughly speaking) similar to vectors, but which change sign under a rotation of radians. ... Given a differentiable manifold M with a tetrad of signature (p,q) over it, a spinor bundle over M is a vector SO(p,q)-bundle over M such that its fiber is a spinor representation of Spin(p,q), the double cover of the special orthogonal group SO(p... In mathematics and physics, an anyon is a type of projective representation of a Lie group. ... ... A spin structure on a smooth orientable Riemannian manifold is a lift of the principal O(n) bundle associated to its tangent bundle to a principal Spin(n) bundle. ...