"symplectic group" meaning in English

{
  "etymology_text": "So named by German mathematician Hermann Weyl, replacing previous confusing names. More at symplectic.",
  "forms": [
    {
      "form": "symplectic groups",
      "tags": [
        "plural"
      ]
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  "lang_code": "en",
  "pos": "noun",
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      "derived": [
        {
          "word": "compact symplectic group"
        }
      ],
      "examples": [
        {
          "ref": "1985, Roger Howe, “Dual Pairs in Physics: Harmonic Oscillators, Photons, Electrons, and Singletons”, in Mosh Flato, Paul Sally, Gregg Zuckerman, editors, Applications of Group Theory in Physics and Mathematical Physics, American Mathematical Society, page 179:",
          "text": "This representation ω arises by virtue of the existence of an action by automorphisms of the symplectic group on a certain two-step nilpotent group, commonly called the Heisenberg group.\nWeil was of course working in the adelic formalism of modern number theory, so he considered symplectic groups and Heisenberg groups with coefficients in a general local field.",
          "type": "quote"
        },
        {
          "text": "2001, G. Wassermann (translator), V. I. Arnol'd, A. B. Givental', Symplectic Geometry, V. I. Arnol'd, S. P. Novikov (editors), Dynamical Systems IV: Symplectic Geometry and its Applications, Springer, 2nd Edition, page 18,\nThe exponential of an operator gives the exponential mapping H↦exp(H)=∑Hᵏ/k! of the space of Hamiltonian operators to the symplectic group. The symplectic group acts by conjugation on itself and on its Lie algebra."
        },
        {
          "ref": "2012, Rolf Berndt, Ralf Schmidt, Elements of the Representation Theory of the Jacobi Group, Springer, page v:",
          "text": "The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group.",
          "type": "quote"
        }
      ],
      "glosses": [
        "For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F."
      ],
      "id": "en-symplectic_group-en-noun-ZWYTtYwh",
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      "raw_glosses": [
        "(linear algebra, group theory) For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F."
      ],
      "topics": [
        "group-theory",
        "linear-algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Hermann Weyl"
      ]
    }
  ],
  "word": "symplectic group"
}

{
  "derived": [
    {
      "word": "compact symplectic group"
    }
  ],
  "etymology_text": "So named by German mathematician Hermann Weyl, replacing previous confusing names. More at symplectic.",
  "forms": [
    {
      "form": "symplectic groups",
      "tags": [
        "plural"
      ]
    }
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        {
          "ref": "1985, Roger Howe, “Dual Pairs in Physics: Harmonic Oscillators, Photons, Electrons, and Singletons”, in Mosh Flato, Paul Sally, Gregg Zuckerman, editors, Applications of Group Theory in Physics and Mathematical Physics, American Mathematical Society, page 179:",
          "text": "This representation ω arises by virtue of the existence of an action by automorphisms of the symplectic group on a certain two-step nilpotent group, commonly called the Heisenberg group.\nWeil was of course working in the adelic formalism of modern number theory, so he considered symplectic groups and Heisenberg groups with coefficients in a general local field.",
          "type": "quote"
        },
        {
          "text": "2001, G. Wassermann (translator), V. I. Arnol'd, A. B. Givental', Symplectic Geometry, V. I. Arnol'd, S. P. Novikov (editors), Dynamical Systems IV: Symplectic Geometry and its Applications, Springer, 2nd Edition, page 18,\nThe exponential of an operator gives the exponential mapping H↦exp(H)=∑Hᵏ/k! of the space of Hamiltonian operators to the symplectic group. The symplectic group acts by conjugation on itself and on its Lie algebra."
        },
        {
          "ref": "2012, Rolf Berndt, Ralf Schmidt, Elements of the Representation Theory of the Jacobi Group, Springer, page v:",
          "text": "The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group.",
          "type": "quote"
        }
      ],
      "glosses": [
        "For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F."
      ],
      "links": [
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          "linear algebra",
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          "group theory",
          "group theory"
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        ]
      ],
      "raw_glosses": [
        "(linear algebra, group theory) For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F."
      ],
      "topics": [
        "group-theory",
        "linear-algebra",
        "mathematics",
        "sciences"
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  "word": "symplectic group"
}