$\mathrm{SU}(2)$Special unitary group

2 × 2 complex unitary matrices of determinant 1

• Lie Groups and Lie AlgebrasSections 6.1–6.3: classical matrix groups and their Lie algebrasOpen source

3

• Lie Groups and Lie AlgebrasSections 6.1–6.3: su(2) consists of traceless skew-Hermitian 2 × 2 matrices; real dimension 2²−1=3Open source

ℤ₂

• Math 210C. Centers of simply connected semisimple groupsPages 1–2: type A₁ and SU(2) center μ₂Open source

0

• Lie Groups and Lie AlgebrasSection 4.17, printed page 31: SU(2)/U(1) and SO(3)/SO(2) as S²; SU(2)=S³ and SO(3)=RP³Open source
• Conrad and Landesman · Compact Lie groupsLecture 16, including (16.6), and Appendix P: Spin(n) as the simply connected double cover for n ≥ 3Open source

Yes

• Lie Groups and Lie AlgebrasSections 6.1–6.3: classical matrix groups and their Lie algebrasOpen source

Yes

• Conrad and Landesman · Compact Lie groupsLectures 26–28 and Appendix V: compact semisimple groups and highest weightsOpen source
• Conrad and Landesman · Compact Lie groupsLecture 16, printed page 73: SU(n) and Sp(n) are simply connectedOpen source

1

• Conrad and Landesman · Compact Lie groupsLecture 25 and Appendix T: root systems and classical root computationsOpen source

Highest weight n = 2j ≥ 0; dimension n + 1. Even n has real type, odd n quaternionic type.

• Lie Groups and Lie AlgebrasSection 11.4: irreducible sl(2,C) modules of highest weight n and dimension n+1Open source
• Lecture 6: Maximal Root, Exponents, Coxeter Numbers, Dual RepresentationsSection 32.5, Example 32.13, printed page 176: even n has real type and odd n has quaternionic typeOpen source

SU(2) is diffeomorphic to S³. The central quotient by {±I} is SO(3).

• Lie Groups and Lie AlgebrasSection 4.17, printed page 31: SU(2)/U(1) and SO(3)/SO(2) as S²; SU(2)=S³ and SO(3)=RP³Open source

Angular momentum, spin, weak isospin, and the basic example of a spin cover.

• Lie Groups and Lie AlgebrasSection 11.4: irreducible sl(2,C) modules of highest weight n and dimension n+1Open source
• Lecture 6: Maximal Root, Exponents, Coxeter Numbers, Dual RepresentationsSection 32.5, Example 32.13, printed page 176: even n has real type and odd n has quaternionic typeOpen source

group:so-3

• Lie Groups and Lie AlgebrasSections 6.1–6.3: classical matrix groups and their Lie algebrasOpen source

group:q-8

• Lie Groups and Lie AlgebrasSections 6.1–6.3: classical matrix groups and their Lie algebrasOpen source

group:su-3

• Lie Groups and Lie AlgebrasSections 6.1–6.3: classical matrix groups and their Lie algebrasOpen source

algebra:su-2-r

• Lie Groups and Lie AlgebrasSections 6.1–6.3: classical matrix groups and their Lie algebrasOpen source
• Lecture 15: Classification of Real Forms of Semisimple Lie AlgebrasSections 41.2–41.4: compact, split, and classical real formsOpen source

real-form:su-2-r

• Lecture 15: Classification of Real Forms of Semisimple Lie AlgebrasSections 41.2–41.4: compact, split, and classical real formsOpen source

map:su-2-to-so-3

• Sporadic isogenies to orthogonal groupsSection 2.1: SU(2) → SO(3), construction and kernelOpen source

map:su-2-to-su-3-regular

• Haber · Spin covers and subgroup examplesProblem 5, pages 14–15: block SU(2) subgroup of SU(3)Open source

map:su-2-to-su-3-principal

• Haber · Spin covers and subgroup examplesProblem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) imageOpen source

map:u-1-to-su-2

• Lie Groups and Lie AlgebrasSections 6.1–6.3: classical matrix groups and their Lie algebrasOpen source
• Lie Groups and Lie AlgebrasSection 4.17, printed page 31: SU(2)/U(1) and SO(3)/SO(2) as S²; SU(2)=S³ and SO(3)=RP³Open source

space:su-2-over-u-1

• Lie Groups and Lie AlgebrasSection 4.17, printed page 31: SU(2)/U(1) and SO(3)/SO(2) as S²; SU(2)=S³ and SO(3)=RP³Open source