# symplectic

## English

edit### Etymology

editA 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

edit### Adjective

edit**symplectic** (*not comparable*)

- Placed in or among, as if woven together.
- (group theory, of a group) Whose characteristic abelian subgroups are cyclic.
- (mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate.
- (mathematics, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form.
- (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*, Springer Science & Business Media (Birkhäuser).**Symplectic**View of Physics**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 .

- That moves in the same direction as a system of synchronized waves.
- (petrology, mineralogy) Of or pertaining to a symplectite; symplectitic.

#### Antonyms

edit#### Derived terms

edit- microsymplectic
- symplectic cut
- symplectic form (symplectic bilinear form)
- symplectic group
- symplectic invariant (structure that is invariant under a symplectic form (regarded as a mapping))
- symplectic matrix
- symplectic Clifford algebra

#### Related terms

edit### Noun

edit**symplectic** (*plural* **symplectics**)

- (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.

- (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

edit- The Classical Groups. Their Invariants and Representations, Hermann Weyl; Princeton University Press, 1939 →ISBN, footnote, p. 165
- The Symplectization of Science, Mark J. Gotay and James A. Isenberg, p. 13

### Further reading

edit-
**symplectic**on Wikipedia.Wikipedia -
**symplectic bone**on Wikipedia.Wikipedia -
**Symplectic cut**on Wikipedia.Wikipedia -
**Symplectic geometry**on Wikipedia.Wikipedia -
**Symplectic group**on Wikipedia.Wikipedia -
**Symplectic manifold**on Wikipedia.Wikipedia -
**Symplectic matrix**on Wikipedia.Wikipedia -
**Group of symplectic type**on Wikipedia.Wikipedia

Categories:

- English terms derived from Ancient Greek
- English 3-syllable words
- English terms with IPA pronunciation
- Rhymes:English/ɛktɪk
- Rhymes:English/ɛktɪk/3 syllables
- English lemmas
- English adjectives
- English uncomparable adjectives
- en:Group theory
- en:Mathematics
- English terms with quotations
- en:Petrology
- en:Mineralogy
- English nouns
- English countable nouns
- en:Ichthyology
- English terms prefixed with sym-