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Spin group

In mathematics the spin group, denoted 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)

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Overview

Use for physics models

Construction

Double covering

Spinor space

Complex case

Exceptional isomorphisms

Indefinite signature

Topological considerations

Quotient groups

Whitehead tower

Discrete subgroups

Related groups

Advanced semantic analysis

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Map overview Semantic statistics

Spin group

Nodes110
Edges109
Triples67
Avg. degree1.98
Density0.018182
Components1

How this topic connects Entity context

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Spin group

Top relations

related to Geometric construction · 12
Spin group → As, Call, Clifford, It, Its, Lie, Since Spin, SO, Spin, The, Then, These
related to Exceptional isomorphisms · 9
Spin group → Cl, Dynkin, For, In, Lie, Rn, Spin, There, Writing
related to Whitehead tower · 8
Spin group → Eilenberg, Killing, MacLane, Spin, String, The, This, Whitehead
related to Construction · 7
Spin group → Cl, Clifford, Construction, Spin, The, The Clifford, TV
related to Indefinite signature · 7
Spin group → As, Clifford, For, In, It, SO, Spin
related to Discrete subgroups · 6
Spin group → Discrete, Galois, Given, SO, Spin, These
related to Use for physics models · 6
Spin group → Dirac, Its, Riemannian, Spinc, Strictly, The
related to External links · 5
Spin group → A096336, A280191, Grothendieck's, OEIS, The
related to Quotient groups · 5
Spin group → If, Lie, Quotient, Quotienting, Spin
is a · 1
Spin group → structure group of a spinor bundle

Important terminology Word statistics

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Important terminology

spin displaystyle group groups algebra operatorname connected clifford given lie space cover spinor orthogonal double quotient subgroup cl center isomorphisms

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Spin groupis astructure group of a spinor bundle0.90text
Spin grouprelated to CenterThe0.60section
Spin grouprelated to ConstructionConstruction0.60section
Spin grouprelated to ConstructionSpin0.60section
Spin grouprelated to ConstructionClifford0.60section
Spin grouprelated to ConstructionThe Clifford0.60section
Spin grouprelated to ConstructionTV0.60section
Spin grouprelated to ConstructionThe0.60section
Spin grouprelated to ConstructionCl0.60section
Spin grouprelated to Discrete subgroupsDiscrete0.60section
Spin grouprelated to Discrete subgroupsGiven0.60section
Spin grouprelated to Discrete subgroupsSpin0.60section

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