English

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Etymology

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A calque of complex, coined by Hermann Weyl in his 1939 book The Classical Groups: Their Invariants and Representations. From Ancient Greek συμπλεκτικός (sumplektikós), from συμ (sum) (variant of σύν (sún)), + πλεκτικός (plektikós) (from πλέκω (plékō)); modelled on complex (from Latin complexus (braided together), from com- (together) + plectere (to weave, braid)).

The symplectic group has previously been called the line complex group.

Pronunciation

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Adjective

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symplectic (not comparable)

  1. Placed in or among, as if woven together.
  2. (group theory, of a group) Whose characteristic abelian subgroups are cyclic.
  3. (mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate.
  4. (mathematics, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form.
  5. (mathematics) Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.
    • 1995, V. I. Arnold, “Some remarks on symplectic monodromy of Milnor fibrations”, in Helmut Hofer, Clifford H. Taubes, Alan Weinstein, Eduard Zehnder, editors, The Floer Memorial Volume, Birkhäuser Verlag, page 99:
      There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.
    • 1997, C. H. Cushman-de Vries (translator), Richard H. Cushman, Gijs M. Tuynman (translation editors), Jean-Marie Souriau, Structure of Dynamical Systems: A Symplectic View of Physics, Springer Science & Business Media (Birkhäuser).
    • 2003, Fabrizio Catanese, Gang Tian (editors), Symplectic 4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E Summer School, Springer, Lecture Notes in Mathematics No. 1938.
    • 2003, Yakov Eliashberg, Boris A. Khesin, François Lalonde, editors, Symplectic and Contact Topology: Interactions and Perspectives, American Mathematical Society:
    • 2003, Maung Min-Oo, “The Dirac Operator in Geometry and Physics”, in Steen Markvorsen, Maung Min-Oo, editors, Global Riemannian Geometry: Curvature and Topology, Springer, page 72:
      In symplectic geometry, there is a notion of fibrations   with a symplectic manifold F as fiber, where the structure group is the group of (exact) Hamiltonian symplectomorphisms of the fiber. These are called symplectic fibrations. If the base manifold   is also symplectic, there is a weak coupling construction, originally due to Thurston, of defining a symplectic structure on the total space  .
  6. That moves in the same direction as a system of synchronized waves.
  7. (petrology, mineralogy) Of or pertaining to a symplectite; symplectitic.

Antonyms

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Derived terms

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Noun

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symplectic (plural symplectics)

  1. (mathematics) A symplectic bilinear form, manifold, geometry, etc.
    • 1967, Journal of Mathematics and Mechanics, volume 16, number 1, Indiana University, page 339:
      The structure of stable symplectics on finite dimensional spaces has been studied by Krein [8], Gelfand & Lidskii [9], and Moser [10] in work of considerable practical importance.
  2. (ichthyology) A bone in the teleostean fishes that forms the lower ossification of the suspensorium, and which articulates below with the quadrate bone by which it is firmly held.
    • 1914, The Philippine Journal of Science, Volume 9, page 27:
      The symplectics (9) consist of a somewhat curved central triangular portion with the base upward, and anteriorly and posteriorly from this extends a wing-like process.
    • 1965, Agra University Journal of Research: Science, Volume 14, page 71:
      The symplectics (Fig. 8, sym) are thin slender bones placed vertically in between the quadrates and the hyomandibulars.
    • 1967, Tyson R. Roberts, Studies on the Osteology and Phylogeny of Characoid Fishes, page 59:
      In many teleosts, on the other hand, including the catfishes, the symplectics have been entirely lost.

References

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Further reading

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