 Spin group

The spin group $\mathrm{Spin}(n)$ is the connected double cover of $SO(n)$ constructed inside the units of a Clifford algebra.

The Spin group is a type of mathematical group that plays a key role in the field of theoretical physics and geometry, particularly in the study of rotations and angular momentum in quantum mechanics and the theory of relativity. 1. **Definition**: The Spin group, often denoted as \( \text{Spin}(n) \), is the double cover of the special orthogonal group \( \text{SO}(n) \).