English Explanatory Dictionary

symplectic

English dictionary entry

Meanings

adj
  1. Placed in or among, as if woven together.
  2. Whose characteristic abelian subgroups are cyclic.
  3. That is alternating and nondegenerate.
  4. That is equipped with an alternating nondegenerate bilinear form.
  5. Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.
  6. That moves in the same direction as a system of synchronized waves.
  7. Of or pertaining to a symplectite; symplectitic.
noun
  1. A symplectic bilinear form, manifold, geometry, etc.
  2. 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.

Pronunciation

/sɪmˈplɛktɪk/

Word forms

symplectic symplectics

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.

Antonyms

antiplectic

Related words

symplectomorphism

Derived words

cosymplectic hyosymplectic microsymplectic multisymplectic nonsymplectic orthosymplectic polysymplectic presymplectic slimplectic subsymplectic supersymplectic symplectically symplectic Clifford algebra symplectic cut symplectic form symplectic group symplectic invariant symplecticity symplectic matrix
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