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”)). In both cases the suffix is from Proto-Indo-European *plek-.
The symplectic group had previously been called the line complex group.
symplectic (not comparable)
- (mathematics) Describing the geometry of differentiable manifolds equipped with a closed, nondegenerate bilinear form.
- The Classical Groups. Their Invariants and Representations, Hermann Weyl; Princeton University Press, 1939 ISBN 978-0-691-05756-9, footnote, p. 165
- The Symplectization of Science, Mark J. Gotay and James A. Isenberg, p. 13