Contents

group theory

Contents

Idea

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

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

References

• 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.