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    "symbol": "Sp(2) → SO(5)",
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    "level": "reference",
    "aliases": [],
    "searchTerms": [],
    "tags": [
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    "summary": "A acts by X ↦ AXA† on the real five-dimensional space of traceless Hermitian quaternionic 2 × 2 matrices. The determinant is a definite quadratic form up to overall sign. Kernel: {±I} ≅ C₂.",
    "definition": "A acts by X ↦ AXA† on the real five-dimensional space of traceless Hermitian quaternionic 2 × 2 matrices. The determinant is a definite quadratic form up to overall sign.",
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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."
    },
    {
      "id": "garrett-isogenies",
      "title": "Sporadic isogenies to orthogonal groups",
      "authors": [
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      ],
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      "locatorHint": "May 7, 2015 notes, Sections 2.1–2.11. The linked file is an accessible mirror of the author’s notes.",
      "licenseNote": "Author’s lecture notes linked at an accessible mirror. No redistribution license is inferred; matrix constructions are explained independently."
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