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
Famous quotes containing the word group:
“Even in harmonious families there is this double life: the group life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”
—Willa Cather (1873–1947)