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    "name": "Adjoint central quotient of SL(2,R)",
    "symbol": "SL(2, R) → PSL(2, R)",
    "category": "lie",
    "level": "reference",
    "aliases": [],
    "searchTerms": [],
    "tags": [
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    ],
    "summary": "A ↦ its central coset; equivalently use conjugation on real traceless 2 × 2 matrices with determinant as an invariant quadratic form. Kernel: {±I} ≅ C₂.",
    "definition": "A ↦ its central coset; equivalently use conjugation on real traceless 2 × 2 matrices with determinant as an invariant quadratic form.",
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      "id": "etingof-global-forms",
      "title": "Lecture 17: Classification of Connected Compact and Complex Reductive Groups",
      "authors": [
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      ],
      "url": "https://ocw.mit.edu/courses/18-755-lie-groups-and-lie-algebras-ii-spring-2024/mit18_755_s24_lec17.pdf",
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      "licenseNote": "Linked MIT OpenCourseWare notes; global-form and representation criteria are restated."
    },
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      "title": "Sporadic isogenies to orthogonal groups",
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