symplectic
Language: English
Part of speech: adj
Pronunciation: ipa: /sɪmˈplɛktɪk/
rhymes: -ɛktɪk
Etymology: 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.
Senses: glosses: Placed in or among, as if woven together.
topics: group-theory
mathematics
sciences
glosses: Whose characteristic abelian subgroups are cyclic.
raw_tags: of a group
topics: mathematics
sciences
qualifier: multilinear algebra
glosses: That is alternating and nondegenerate.
raw_tags: of a bilinear form
topics: mathematics
sciences
qualifier: multilinear algebra
glosses: That is equipped with an alternating nondegenerate bilinear form.
raw_tags: of a vector space
examples: text: There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.
ref: 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:
text: 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).
text: 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.
ref: 2003, Yakov Eliashberg, Boris A. Khesin, François Lalonde, editors, Symplectic and Contact Topology: Interactions and Perspectives, American Mathematical Society:
text: In symplectic geometry, there is a notion of fibrations #92;pi#58;P#92;rightarrowM 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 (M,#92;omega#95;M) is also symplectic, there is a weak coupling construction, originally due to Thurston, of defining a symplectic structure on the total space P.
ref: 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:
topics: mathematics
sciences
glosses: Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.
glosses: That moves in the same direction as a system of synchronized waves.
topics: chemistry
geography
geology
mineralogy
natural-sciences
petrology
physical-sciences
glosses: Of or pertaining to a symplectite; symplectitic.
Derived terms: word: microsymplectic
word: symplectic Clifford algebra
word: symplectic cut
english: symplectic bilinear form
translation: symplectic bilinear form
word: symplectic form
word: symplectic group
english: structure that is invariant under a symplectic form (regarded as a mapping)
translation: structure that is invariant under a symplectic form (regarded as a mapping)
word: symplectic invariant
word: symplectic matrix
Related terms: symplectomorphism