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    "name": "Projective special unitary group",
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    "category": "lie",
    "level": "executable",
    "aliases": [
      "SU(3)/Z3"
    ],
    "searchTerms": [
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    ],
    "tags": [
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      "Global form"
    ],
    "summary": "The adjoint compact group SU(3)/ℤ₃. It shares its Lie algebra with SU(3), with a different global form.",
    "definition": "SU(3) modulo scalar cube roots of unity",
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        "source": "conrad-centers",
        "locator": "Pages 2–4: centers of simply connected groups by root-system type"
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        "source": "conrad",
        "locator": "Appendix O, pages 231–232: fundamental groups and covering groups; Appendix V: central quotients"
      }
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        "label": "Center",
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            "locator": "Section 43.1: the compact adjoint form has trivial center"
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        "value": "ℤ₃",
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            "source": "conrad-centers",
            "locator": "Pages 2–4: centers of simply connected groups by root-system type"
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            "source": "conrad",
            "locator": "Appendix O, pages 231–232: fundamental groups and covering groups; Appendix V: central quotients"
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        "assumptions": []
      },
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        "key": "compact",
        "label": "Compact",
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            "source": "conrad",
            "locator": "Lectures 26–28 and Appendix V: compact semisimple groups and highest weights"
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            "source": "conrad",
            "locator": "Lecture 16, printed page 73: SU(n) and Sp(n) are simply connected"
          }
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        "assumptions": []
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        "key": "connected",
        "label": "Connected",
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            "source": "conrad",
            "locator": "Lectures 26–28 and Appendix V: compact semisimple groups and highest weights"
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            "source": "conrad",
            "locator": "Lecture 16, printed page 73: SU(n) and Sp(n) are simply connected"
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        "assumptions": []
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        "key": "rank",
        "label": "Rank",
        "value": "2",
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                "locator": "Section 27.2: the two A₂ fundamental modules have scalar charges 1 and 2"
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        "paragraphs": [
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            "text": "The covering SU(3) → PSU(3) has kernel ℤ₃, which is the fundamental group of PSU(3).",
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                "locator": "Appendix O, pages 231–232: fundamental groups and covering groups; Appendix V: central quotients"
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        "id": "physics",
        "title": "In physics",
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        "id": "weight-convention",
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            "text": "The labels (p,q) mean λ = pω₁ + qω₂, with (1,0) the defining 3 and (0,1) its conjugate. The scalar center generator exp(2πi/3)I acts with charge p + 2q modulo 3.",
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        "label": "Actual real Lie algebra",
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