nLab quaternionic unitary group


See also compact symplectic group.



This Lie group is the analog of the unitary group as one passes from the complex numbers to the quaternions.

The quaternionic unitary group Sp(n)Sp(n) is the group of quaternion-unitary transformations of n\mathbb{H}^n. It is also called the compact symplectic group, since both it and the symplectic group Sp(2n,)Sp(2n, \mathbb{R}) are real forms of the complex Lie group Sp(2n,)Sp(2n,\mathbb{C}), and it is the compact form.


Exceptional isomorphisms


  • Quaternionic groups (pdf)

Last revised on January 18, 2023 at 21:26:23. See the history of this page for a list of all contributions to it.