In mathematics, the name symplectic group can refer to two different, but closely related, types of mathematical groups, denoted Sp(2n, F) and Sp(n). The latter is sometimes called the compact symplectic group to distinguish it from the former. Many authors prefer slightly different notations, usually differing by factors of 2. The notation used here is consistent with the size of the matrices used to represent the groups. In Cartan's classification of the simple Lie algebras, the Lie algebra of the complex group Sp(2n, C) is denoted Cn, and Sp(n) is the compact real form of Sp(2n, C).
The name "symplectic group" is due to Hermann Weyl (details) as a replacement for the previous confusing names of (line) complex group and Abelian group, and is the Greek analog of "complex".
Read more about Symplectic Group: Sp(2n, F), Sp(n), Relationships Between The Symplectic Groups, Important Subgroups, Example of Symplectic Matrices, Infinitesimal Generators
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