[Math] What does the word “symplectic” mean

etymologysg.symplectic-geometrysoft-question

I know the definition of symplectic structure, symplectic group, and so on. But what does the word "symplectic" itself mean?

Meta question: I have many other mathematical words whose etymologies are obscure to me. Is it OK for me to ask one question per such word?

Best Answer

The term "symplectic group" was suggested in The Classical Groups: their invariants and representations (1939, p. 165) by Herman Weyl:

The name "complex group" formerly advocated by me in allusion to line complexes, as these are defined by the vanishing of antisymmetric bilinear forms, has become more and more embarrassing through collision with the word "complex" in the connotation of complex number. I therefore propose to replace it by the corresponding Greek adjective "symplectic." Dickson calls the group the "Abelian linear group" in homage to Abel who first studied it.

Take a look at the Earliest Known Uses of Some of the Words of Mathematics web page.

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