symplectic

== English == === 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. === Pronunciation === IPA(key): /sɪmˈplɛktɪk/ Rhymes: -ɛktɪk === Adjective === 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. 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. That moves in the same direction as a system of synchronized waves. (petrology, mineralogy) Of or pertaining to a symplectite; symplectitic. ==== Antonyms ==== antiplectic ==== Derived terms ==== ==== Related terms ==== symplectomorphism === Noun === symplectic (plural symplectics) (mathematics) A symplectic bilinear form, manifold, geometry, etc. (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. === References === 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 === 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